To find the maximum likelihood estimator (MLE) of the parameter λ in an exponential distribution, given a random sample X₁, X₂, ..., Xₙ, we can apply the MLE method.
(a) To find the MLE of the parameter λ in the exponential distribution, we construct the likelihood function based on the sample X₁, X₂, ..., Xₙ. The likelihood function is the product of the density functions of each observation. Taking the logarithm of the likelihood function, we simplify the maximization process. By differentiating the logarithm of the likelihood function with respect to λ and setting it equal to zero, we can solve for the MLE of λ, denoted as Ȧ.
(b) To find the MLE of the median m, we construct the likelihood function based on the sample X₁, X₂, ..., Xₙ, similar to the previous case. However, the median is not a parameter of the exponential distribution, so we need to transform the problem. We can define two probabilities: P(X₁ ≤ m) and P(X₁ ≥ m). Setting these probabilities equal to 0.5 each, we can obtain two equations involving λ and m. By solving these equations simultaneously, we can find the MLE of the median m.
In summary, to find the MLE of the parameter λ in an exponential distribution, we maximize the likelihood function using the given sample. Similarly, to find the MLE of the median m, we set the probabilities involving m equal to 0.5 and solve the resulting equations. These estimators provide the maximum likelihood estimates for λ and m based on the observed data.
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A compact disc is designed to last an average of 4 years with a standard deviation of 0.8 years. What is the probability that a CD will last less than 3 years?
A- 1.11%, B - 10.56%, C - 86.65%, D - 100%
Answer:
the answer is B.........................
A study conducted by an airline showed that a random sample of 120 of its passengers arriving at Kennedy Airport on flights from Europe took an average of 24.15 minutes with a standard deviation of 3.29 minutes to claim their baggage and clear customs. What can the airline say with 95% confidence about the maximum error, if it uses x = 24.15 minutes as an estimate of the true average time that one of its passengers arriving at Kennedy Airport on a flight from Europe requires to claim his ticket? baggage and pass customs.?
The airline can say with 95% confidence that the maximum error in using x = 24.15 minutes as an estimate of the true average time is 24.736.
How do we solve confidence interval for the True average time?To calculate the confidence interval, we used the following formula:
CI = x ± z × SE.
CI is the confidence interval
x is the sample mean
z is the z-score for the desired confidence level (in this case, 95%)
SE is the standard error of the mean
The z-score for a 95% confidence interval is 1.95. ⇒ 0.05/2 = 0.025 = 1.95.
the sample standard deviation is 3.29 and the sample size is 120.
Therefore
CI = 24.15 + 1.95 × 3.29 / √(120) = 24.736
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find the value of x to the nearest tenth
Answer:
114
Step-by-step explanation:
You would add 46 degree and 20 degrees (66) and subtract (180 - 66 = ?) to get your answer.
Answer:
114
Step-by-step explanation:
Two mechanics were working on your car. One can complete the given job
in six hours, but the new guy takes eight hours. They worked together for
the first two hours, but then the first guy left to help another mechanic on
a different job. How long will it take the new guy to finish your car?
PLS EXPLAIN YOUR WORK AND SHOW YOUR STEPS CLEARLY
It will take the new guy approximately 3.33 hours to finish your car.To find out how long it will take the new mechanic to finish the car, we need to consider their individual rates of work.
Let's denote the first mechanic's rate as "M1" (job per hour) and the new guy's rate as "M2" (job per hour).
We are given that M1 can complete the job in six hours, so his rate of work is 1/6 of the job per hour. Similarly, the new guy takes eight hours to complete the job, so his rate of work is 1/8 of the job per hour.
When they worked together for the first two hours, they combined their rates of work. So in the first two hours, they completed (2/6 + 2/8) of the job.
Now, the first mechanic leaves and only the new guy is left to finish the remaining portion of the job. Let's denote the time it takes for the new guy to complete the remaining portion as "T."
Since we know the portion of the job completed in the first two hours, we can set up the equation: (2/6 + 2/8) + (T/8) = 1.
Simplifying the equation, we have (8/24 + 6/24) + (T/8) = 1.
Combining the fractions, we get 14/24 + (T/8) = 1.
Subtracting 14/24 from both sides, we have T/8 = 10/24.
Simplifying further, we find T = (10/24) * 8 = 3.33 hours.
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solve for x round to your nearest tenth
Given the data 21, 13, 13, 37, 13, 23, 25, 15: What is the outlier in the data? What is the mean with the outlier? What is the mean without the outlier? A. 13; 21; 17.6 B. 37; 20; 17.6 C. 37; 17.6; 20 D. 13; 17.6; 21
A window is designed as shown below. Find the value of x
Answer:
x=20
Step-by-step explanation:
We know that a line is 180 degrees, and the base of the cemi-circle is a line. So, we would have:
x+7x+x=180
9x=180
x=20
Hope this helps!!
Answer:
x = 20
Step-by-step explanation:
x + 7x + x = 180
9x = 180
x = 20
name a pear of lines that apper to be parallel
Consider f: R2 + R² given by (x,y) → (3x + 2y, 7.x + 5y). . Is f injective? Is f surjective? • Does f have an inverse and if yes what is it?
To determine if f has an inverse, we need to check if it is bijective (both injective and surjective). Since f is not injective, it cannot have an inverse.
To determine whether the function f: R^2 -> R^2 given by (x, y) -> (3x + 2y, 7x + 5y) is injective (one-to-one) and surjective (onto), we need to analyze its properties.
Injectivity:
A function f: A -> B is injective if for every pair of distinct elements in A, their corresponding images in B are also distinct. In other words, if f(x) = f(y), then x = y.
Let's consider two distinct points in R^2: (x1, y1) and (x2, y2). If f(x1, y1) = f(x2, y2), we have:
(3x1 + 2y1, 7x1 + 5y1) = (3x2 + 2y2, 7x2 + 5y2)
By comparing the corresponding components, we get the following system of equations:
3x1 + 2y1 = 3x2 + 2y2 (Equation 1)
7x1 + 5y1 = 7x2 + 5y2 (Equation 2)
We can subtract Equation 1 from Equation 2 to eliminate the variables:
7x1 + 5y1 - (3x1 + 2y1) = 7x2 + 5y2 - (3x2 + 2y2)
4x1 + 3y1 = 4x2 + 3y2
Rearranging the equation gives:
4x1 - 4x2 = 3y2 - 3y1
4(x1 - x2) = 3(y2 - y1)
Since this equation holds for any values of x1, x2, y1, and y2, it implies that the difference in the x-coordinates must be the same as the difference in the y-coordinates for any two distinct points. However, this is not always true, indicating that f is not injective. Therefore, the function is not one-to-one.
Surjectivity:
A function f: A -> B is surjective if every element in the codomain B has a preimage in the domain A. In other words, for every element b in B, there exists an element a in A such that f(a) = b.
To determine surjectivity, we need to find whether there exists an (x, y) in R^2 such that f(x, y) = (a, b) for any (a, b) in R^2.
Let's take an arbitrary point (a, b) in R^2. We need to find an (x, y) such that:
(3x + 2y, 7x + 5y) = (a, b)
This gives us a system of equations:
3x + 2y = a (Equation 3)
7x + 5y = b (Equation 4)
We have two equations with two variables, which can be solved to find the values of x and y. Since the system has a unique solution for every (a, b) in R^2, we can conclude that f is surjective.
Inverse:
To determine if f has an inverse, we need to check if it is bijective (both injective and surjective). Since f is not injective, it cannot have an inverse.
In summary:
The function f: R^2 -> R^2 given by (x, y) -> (3x + 2y, 7x.
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Factor the expression (s):
7x+63
12x+15
36z+60
probablity question: A bag contains 4 red marbles, 3 blue marbles and 7 green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest 10th of a percent, that all three marbles drawn will be green?
Answer: 12.5%
Step-by-step explanation:
i dunno for sure so probably use someone elses answer
What is the quotient of 1/6 divided by 5?
Answer:
0.03333333333 = 33/1000 = 3.3%
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
Identify the Type I and Type 2 error for the following claim
(a) The average time that customers wait on hold for customer wrvice at a certain company in less than 5 minutes
(b) The number of salespeople employed at a car lot in linearly correlated with the annual profit of the lot.
(a) Type I error: Rejecting the claim , Type II error: Failing to reject the claim. (b) Type I error: Rejecting the claim, Type II error: Failing to reject the claim.
For claim (a):
Type I error: Rejecting the claim that the average time customers wait on hold is less than 5 minutes when, in fact, it is true. This means concluding that the average wait time is longer than 5 minutes when it is not.
Type II error: Failing to reject the claim that the average time customers wait on hold is less than 5 minutes when, in fact, it is false. This means concluding that the average wait time is less than 5 minutes when it is actually longer.
For claim (b):
Type I error: Rejecting the claim that the number of salespeople employed at a car lot is linearly correlated with the annual profit of the lot when, in fact, it is true. This means concluding that there is no linear correlation between the number of salespeople and annual profit when there actually is.
Type II error: Failing to reject the claim that the number of salespeople employed at a car lot is linearly correlated with the annual profit of the lot when, in fact, it is false. This means concluding that there is a linear correlation between the number of salespeople and annual profit when there actually isn't.
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PLEASE HELP WITH THIS QUESTION!!
NO LINKS PLEASE
Answer:
Step-by-step explanation:
g(x)=[x-4] h(x)= [x] -5
h= -5
g=[x-4]
x x
g=4
A computer tablet is 0.24 meter long. How long is the computer tablet in centimeters?
Answer:
24 cm long
Step-by-step explanation:
Gigi's Family left their house and drove 14 miles south to a gas station and then 48 miles east to a waterpark. How much shorter with their trip to the waterpark have been if they hadn't stopped at the gas station and had driven along the diagonal path instead?
Answer:
If they hadn't stopped at the gas station and had driven along the diagonal path, their trip would have been 12 miles shorter.
Step-by-step explanation:
Given that Gigi's Family left their house and drove 14 miles south to a gas station and then 48 miles east to a waterpark, to determine how much shorter would their trip to the waterpark have been if they hadn't stopped at the gas station and had driven along the diagonal path instead the following calculation must be performed, using the Pythagorean theorem:
14 ^ 2 + 48 ^ 2 = X ^ 2
196 + 2,304 = X ^ 2
√ 2500 = X
50 = X
14 + 48 - 50 = X
62 - 50 = X
Thus, if they hadn't stopped at the gas station and had driven along the diagonal path, their trip would have been 12 miles shorter.
IVE BEEN STUCK ON THIS FOR AN HOUR PLEASE HELP WHAT IS 9.85714285714 X 7
Answer:
69
Step-by-step explanation:
lol
WHAT IS THE PROBABILITY OF LANDING ON TAILS ON THE FIRST FLIP AND THEN TAILS AGAIN ON THE SECOND FLIP?
Answer:
25%
Since it's 2 in a row, it is divided by 4
technically it depends on the way you flip the coin, its mostly a 50-50
a more answer-y answer to this would be around (heads) 65-35 (tails) in my opinion.
If using the method of completing the square to solve the quadratic equation x^2-3x+20=0x 2 −3x+20=0, which number would have to be added to "complete the square"?
Answer:
The polynomial must be added by 2.25 on each side of the equation.
Step-by-step explanation:
Let [tex]x^{2}-3\cdot x +20 = 0[/tex], we need to add each side by 2.25 to complete the square, that is, expanding the polynomial so that factor of a perfect square trinomial can be done:
1) [tex]x^{2}-3\cdot x +20 = 0[/tex] Given
2) [tex](x^{2}-3\cdot x +20) +2.25 = 2.25 + 0[/tex] Compatibility with addition/Commutative property
3) [tex](x^{2}-3\cdot x +2.25) +20 = 2.25[/tex] Commutative, associative and modulative properties.
4) [tex](x-1.5)^{2} +20 = 2.25[/tex] Perfect square trinomial/Result
Answer:
(x−21)^2=81/4
A quantity with an initial value of 400 grows exponentially at a rate such that the quantity doubles every 8 days. What is the value of the quantity after 29 days, to the nearest hundredth?
Observation from two random and independent samples, drawn from population 1 and 2are given below. Use the Wilcoxon rank sum test to determine whether population 1 is shifted to the left of population 2 Sample 1 33 61 20 19 40 Sample 2 26 36 65 25 35 (1) State the null and alternative hypotheses to be tested.
The null hypothesis will be rejected if the test statistic is smaller than the critical value at a given significance level. The following hypotheses to be tested are:
H0: Population 1 = Population 2
H1: Population 1 < Population 2
Null hypothesis: Population 1 and Population 2 are not significantly different in their distributions of observations.
Alternative hypothesis: Population 1 is shifted to the left of Population 2 in their distributions of observations. This is a one-tailed test. Thus, the null hypothesis will be rejected if the test statistic is smaller than the critical value at a given significance level.
Therefore, the following hypotheses are to be tested:
H0: Population 1 = Population 2
H1: Population 1 < Population 2
The null hypothesis is a fundamental concept in statistical hypothesis testing. It is a statement that assumes there is no significant relationship between two variables or no difference between two groups being compared. The null hypothesis is often denoted as H0.
In simpler terms, the null hypothesis suggests that any observed differences or relationships in a study are due to random chance or sampling error rather than a genuine effect. It serves as a basis for comparison against an alternative hypothesis, which proposes a specific relationship or difference.
To conduct a hypothesis test, researchers typically formulate a null hypothesis and an alternative hypothesis. The alternative hypothesis (denoted as Ha or H1) represents the claim they want to support or prove. The null hypothesis, on the other hand, assumes that the alternative hypothesis is false or not valid.
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help. please. I really need help if its correct i would be happy
Answer:
[tex]-22\frac{1}{3}[/tex]
Step-by-step explanation:
[tex]a=\frac{1}{3} , b = -10, c = -3[/tex]
change [tex]b^{2} - 9a^{2} + c[/tex] to
[tex]-10 -9\frac{1}{3} + (-3)[/tex]
=
[tex]-22\frac{1}{3}[/tex]
In 1945, what concern did the Allies have about invading the Japanese mainland with ground forces? They were worried they did not have enough soldiers. They were worried there would be too great a loss of life. They were worried the Japanese were developing an atomic bomb. They were worried the Japanese had a stronger fleet in mainland ports.
Answer:
b
Step-by-step explanation:
i need points
In 1945, the concern which the Allies had about invading the Japanese mainland with ground forces was:
B. They were worried there would be too great a loss of life.What is an Invasion?This refers to a military tactic where the armed forces of a country or a place go into enemy territory with the aim of defeating the troops and claiming the territory.
With this in mind and from the events in history, we can see that after the bombing of Pearl Harbor by the Japanese Navy, there were concern by the Allies of invading the Japanese mainland with ground forces because they feared the great loss of life.
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Perform the following test of hypothesis. H0: μ = 285, H1: μ < 285, n = 55, x = 266.89, s = H0 is
By Performing the following test of hypothesis, H0 is rejected.
To perform the test of hypothesis, we compare the sample mean (x) to the hypothesized population mean (μ) and consider the sample size (n) and sample standard deviation (s).
Given:
H0: μ = 285 (null hypothesis)
H1: μ < 285 (alternative hypothesis)
n = 55 (sample size)
x = 266.89 (sample mean)
s = ?
To determine whether to reject or fail to reject the null hypothesis, we calculate the test statistic and compare it to the critical value or p-value.
Since the standard deviation (s) is not given, we cannot directly calculate the test statistic. Without the value of s, we cannot proceed with the hypothesis test. Please provide the value of s to continue with the calculation and draw a conclusion.
The test of hypothesis cannot be performed without the value of the sample standard deviation (s). Please provide the necessary information to proceed with the calculation and draw a conclusion.
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PLEASE I NEED HELP
uhh whats 1 + 2
I don't get it. I have a feeling its 12 though.
your answer should be 3 :)
What are the solutions to the following system of equations?
y = 3x - 7
5x - y = 11
A(2, -1)
B (3, 4)
C (-3, 3)
D (-6, 1)
Answer:
A (2,-1)
Step-by-step explanation:
-1 = 3(2) -7
5(2) - (-1) = 11
Sonia has two packages of hamburger meat. The first package weighs 1.76 pounds and the second package weighs 2.29 pounds. She mixes the two packages together and forms hamburgers that weigh 0.25 pounds each. What is the greatest number of 0.25- pound hamburgers Sonia can make using the hamburger meat she has?
16 because o.25 times 16 = 4
1.76+2.29=4.05 so 16
Answer:
16.
Step-by-step explanation:
0.25 × 16 = 4
1.76 + 2.29 = 4.05
so the answer is 16
hope this helps!
~mina-san
Question 8 of 10
Which of the following are remote interior angles of Z1? Check all that apply.
ole
O A. 25
B. 21
O c. 26
O D. 24
D E. 23
O F. 22
Answer:
D and E
Step-by-step explanation:
remote interior angles are not adjacent to a given angle. or basically 1 is our exterior angle, so the opposites of 1 and the remote interior angle.
The remote interior angles of Z1 are ∠4 and ∠3. The correct options are D and E.
What are remote interior angle?A triangle's remote interior angles are the two angles that are not adjacent to a given exterior angle. An exterior angle of a triangle is formed by extending one of the triangle's sides.
The following theorem can be used to calculate the remote interior angles of a triangle:
A triangle's remote interior angles are equal in size to the exterior angle that is not adjacent to them.
In other words, if we know the measure of one of a triangle's exterior angles, we can find the measure of the distant interior angles by subtracting that measure from 180 degrees.
Thus, the correct options are D and E.
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Describe the error Sadie made, and explain how to find the correct answer. (Refer to image)
Step 1: Explain the error made
Step 2: Explain how to find the correct answer.
a)Error:multiplied the numerator and denominator by 3 instead of 2.
b)The correct answer to the given expression is 8/15.
In the given image, Sadie made an error in the simplification of the expression.
The error is that she multiplied the numerator and denominator by 3 instead of 2.
She simplified the numerator and the denominator before carrying out multiplication by 2.
This resulted in the final answer being incorrect.
The correct answer would be 8/5.
The correct way to simplify the expression is as follows:
[tex]$$\frac{4}{3} \div \frac{5}{6} = \frac{4}{3} \times \frac{6}{5}$$[/tex]
Now, cross-cancelling can be performed because the numerator of the first fraction and the denominator of the second fraction have a common factor of 2.
[tex]$$=\frac{4 \times 2}{3 \times 5} = \frac{8}{15}$$[/tex]
Therefore, the correct answer to the given expression is 8/15.
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Rectangle ABCD is congruent to rectangle A″B″C″D″ . Which sequence of transformations could have been used to transform rectangle ABCD to produce rectangle A″B″C″D″ ? Rectangle ABCD was reflected across the y-axis and then across the x-axis. Rectangle ABCD was translated 8 units left and then 7 units down. Rectangle ABCD was translated 2 units left and then 3 units down. Rectangle ABCD was rotated 180° around the origin and then translated 7 units down. A coordinate graph with rectangle A B C D and rectangle A double prime B double primes C double prime and D double prime. Rectangle A B C D has points at A begin ordered pair 2 comma 5 end ordered pair, B begin ordered pair 2 comma 2 end ordered pair, C begin ordered pair 6 comma 2 end ordered pair, D begin ordered pair 6 comma 4 end ordered pair. Rectangle A double prime B double prime C double prime D double prime has points at A double prime begin ordered pair negative 6 comma negative 3 end ordered pair, B double prime begin ordered pair negative 6 comma negative 5 end ordered pair, C double prime begin ordered pair negative 2 comma negative 5 end ordered pair, D double prime begin ordered pair negative 2 comma negative 3 end ordered pair