(a) fz (z) and fw (w) in terms of cumulative distribution functions (CDFs) are:
fz(z) = Fx(z) * (1 - Fy(z)) + Fy(z) * (1 - Fx(z))
fw(w) = 1 - fz(w)
(b) If X and Y are independent exponential random variables with parameter λ, then fw(w) = [tex]1 - e^{-2\lambda w}[/tex] for w ≥ 0.
To determine fz(z) and fw(w) in terms of the marginal cumulative distribution functions (CDFs) of X and Y random variables, we need to consider the region of interest on the X-Y plane.
(a) Drawing the region of interest on the X-Y plane:
The region of interest can be visualized as the area where Z = max(X, Y) and W = min(X, Y) take specific values. This region is bounded by the line y = x (diagonal line) and the lines x = z (vertical line) and y = w (horizontal line).
Determining fz(z):
To find fz(z), we need to consider the cumulative probability that Z takes a value less than or equal to z. This can be expressed as:
fz(z) = P(Z ≤ z) = P(max(X, Y) ≤ z)
Since X and Y are independent random variables, the probability can be calculated using the joint CDF of X and Y:
fz(z) = P(max(X, Y) ≤ z) = P(X ≤ z, Y ≤ z)
Using the marginal CDFs of X and Y, denoted as FX(x) and FY(y), respectively, we can express fz(z) as:
fz(z) = P(X ≤ z, Y ≤ z) = P(X ≤ z) * P(Y ≤ z) = FX(z) * FY(z)
Determining fw(w):
To find fw(w), we need to consider the cumulative probability that W takes a value less than or equal to w. This can be expressed as:
fw(w) = P(W ≤ w) = P(min(X, Y) ≤ w)
Since X and Y are independent random variables, the probability can be calculated using the joint CDF of X and Y:
fw(w) = P(min(X, Y) ≤ w) = 1 - P(X > w, Y > w)
Using the marginal CDFs of X and Y, denoted as FX(x) and FY(y), respectively, we can express fw(w) as:
fw(w) = 1 - P(X > w, Y > w) = 1 - [1 - FX(w)][1 - FY(w)]
Special case when X and Y are independent exponential random variables with parameter A:
If X and Y are independent exponential random variables with a common parameter A, their marginal CDFs can be expressed as:
[tex]FX(x) = 1 - e^{-Ax}\\FY(y) = 1 - e^{-Ay}[/tex]
Using these marginal CDFs, we can substitute them into the formulas for fz(z) and fw(w) to obtain the specific expressions for the random variables Z and W.
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The graph of a system of equations is
shown below.
a. (2,0) and (0,3)
b. (-40,-50)
c. the system has no solution
d. the system has infinitely many solutions
Answer:
The system has no solution.
Step-by-step explanation:
In order for the system to have a solution, both graphs must have an intercept to each others. We see in the picture that both graphs are parallel and do not have any interceptions which we don't know the solution to the system.
That means if graphs are parallel and have no interceptions, there are no solutions. The system of equations are for finding the interceptions of both graphs. But of course! Parallel lines do not intercept.
If you have any questions, feel free to ask.
What Statistic information we can get from a histogram?
A-Standard Deviation
B-Interquartile Range
C-Mean
Determine the area and circumference of a circle with radius 12 cm.
The area of the circle is 452.16 cm², and the circumference is 75.36 cm.
To determine the area and circumference of a circle with a radius of 12 cm, we can use the formulas:
Area = π * r²
Circumference = 2 * π * r
The radius (r) is 12 cm, we can substitute this value into the formulas to find the area and circumference.
Area = π * (12 cm)²
= π * 144 cm²
≈ 3.14 * 144 cm²
≈ 452.16 cm²
The area of the circle is approximately 452.16 square centimeters.
Circumference = 2 * π * 12 cm
= 2 * 3.14 * 12 cm
≈ 75.36 cm
The circumference of the circle is approximately 75.36 centimeters.
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To finish a board game Yanis needed to land on the last square rolling a sum of 6 with two dice. She was dismayed that it took her eight tries. Should she have been surprised?
Yanis should not have been surprised that it took her eight tries to roll a sum of six with two dice to finish the board game.
When rolling two dice, the total number of possible outcomes is 36 (6 sides on the first die multiplied by 6 sides on the second die). Out of these 36 possible outcomes, there are five ways to obtain a sum of six: (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1). This means that the probability of rolling a sum of six is 5/36.
Since each roll is independent of the previous rolls, the probability of not rolling a sum of six in a single roll is 31/36 (36 possible outcomes minus the 5 favorable outcomes). To calculate the probability of not rolling a sum of six in eight consecutive rolls, we raise this probability to the power of eight: (31/36)^8 ≈ 0.282.
Therefore, there was approximately a 28.2% chance that Yanis would not roll a sum of six in eight tries. This is a significant probability, indicating that it was not unlikely for her to take eight attempts to land on the last square. Thus, she should not have been surprised by the outcome.
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Simplify
(2½)² x (0,5)²
Answer:
1.5625
Step-by-step explanation:
2½ = 5/2
(5/2)² = 25/4
25/4 = 6.25
0.5² = 0.25
6.25 x 0.25 = 1.5625
The graph solves this system of equations. Enter the solution in the boxes. –2y = –4x + 8 x + y = 5
Answer:
x=2-y/2
Step-by-step explanation:
The solution of system of equations –2y = –4x + 8 and x + y = 5 is (3, 2).
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The given system of equations are –2y = –4x + 8
x + y = 5
x=5-y
Nu=ow plug in this in the first equation
-2y=-4(5-y)+8
-2y=-20+4y+8
Take the variable terms on one side and constant on other side.
-6y=-12
Divide both sides by 6
y=2
Now put in the equation of x
x=5-2=3
Hence, the solution of system of equations –2y = –4x + 8 and x + y = 5 is (3, 2).
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Which statement explains the type of function that is represented by the equation
y=x2 +9?
Find the area of the figure
Answer:
A=153.94
Step-by-step explanation:
7 ⅓ ÷ 225 =
answer this question plz
Answer:
0.03259..
Step-by-step explanation:
The volume of a square pyramid is 48 in^3 with a height of 4 inches. Find the length of one of the side of the base.
Answer:
6 inches
Step-by-step explanation:
area of square = 48 x 3 / 4 = 36 in^2
side = 6 in
Answer:
6 in
Step-by-step explanation:
The volume formula for a square-base pyramid of side length x and height h is V = (1/3)x²h. We want to solve this for the base side length x:
Multiplying both sides by (3/h) results in:
3V
----- = x² and so the side length, x, is √(3V/h).
h
Substituting 4 in for h and 48 in³ for V, we get: x = √(144 in³/4 in) = 6 in
Check: Does the volume formula given above result in 48 in³ when x = 6 in and h = 4 in?
V = (1/3)x²h = (1/3)(6 in)²(4 in) = 48 in³ YES: x = 6 in is correct.
what are the values of a and b? a = 2y and b = 3 a = and b = –3y a = 2y and b = –3 a = and b = 3y
The values of a and b are dependent on the equation. For example, in the equation a = 2y and b = 3, then a = 6 and b = 3. However, in the equation a = 2y and b = -3, then a = -6 and b = -3.
In the given options, the values of a and b are stated as a = 2y and b = –3. This means that the value of a is equal to twice the value of y (a = 2y), and the value of b is equal to -3. The other options do not match these conditions. It is important to note that without further context or information about the variable y, we cannot determine a specific value for a or b. The values provided only establish the relationship between a, b, and y as described in the option a = 2y and b = –3.
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Write and solve an equation to find the missing dimension of the figure.
Answer:
15.5769230769
Step-by-step explanation:
8×13 = 104
1620÷104 = 15.5769230769
My Samsung charger broke so I went to Five Below to get a new one. They were on sale for $15,35 (not so five below). There
was a 6% tax too. How much did the new charger cost?
( I don’t need the explanation, only the right answer)
Answer:
The answer to your question is 16.27
Explanation:
You would start with the equation,
15.35 + 6% = C (Cost)
15.35 · 6% = 0.921
15.35 + 0.921 = 16.271
Round the one down, since it is less than four, and you get 16.27
Hope this helps.
waffletowne
Randomly select a painted rock from a bag containing 4 purple rocks, 3 green rocks, 3 orange rocks, and 2 blue rocks.
Answer:
i got a orange
Step-by-step explanation:
SOMEONE PLS HELP SHEHSJHSHS
Answer:
1. Quadrant II
2. Quadrant IV
3. Y-axis
Step-by-step explanation:
Describe the attributes of An acute triangle: An obtuse triangle: A right triangle: How many equal sides does an equilateral triangle have: isosceles: scalene pls help I will give you 15 pointss
Answer:
An acute triangle - interior angles are always less than 90 degrees with different side measures.
An obtuse triangle - one of the interior angles is more than 90 degrees. if one angle measures more than 90 degrees, then the sum of the remaining two angles is less than 90 degrees.
An right triangle - a triangle with a right angle (90 degrees)
Equilateral triangle has three equal sides. Isosceles triangles has two equal side lengths. Scalene triangles has no equal side lengths
Factor completely x3 − 2x2 − 8x + 16.
(x + 2)(x2 + 8)
(x − 2)(x2 + 8)
(x + 2)(x2 − 8)
(x − 2)(x2 − 8)
The expression x^3 - 2x^2 - 8x + 16 can be factored as (x - 2)(x^2 - 8).
To factor the given expression x^3 - 2x^2 - 8x + 16, we can look for common factors or factor it using grouping. In this case, we can observe that the expression can be factored by grouping.
First, we can factor out a common factor of (x - 2) from the first two terms:
x^3 - 2x^2 - 8x + 16 = (x - 2)(x^2 - 8x - 8)
Now, we can further factor the quadratic expression (x^2 - 8x - 8) by factoring out a common factor of 8:
(x^2 - 8x - 8) = (x - 2)(x - 8)
Therefore, the complete factorization of the expression x^3 - 2x^2 - 8x + 16 is:
(x - 2)(x - 2)(x - 8) which can also be written as (x - 2)(x^2 - 8).
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Find the volume of each composite figure.
Answer:
630 in^3
Step-by-step explanation:
6 x 6 x 14 = 504
(0.5 x 3 x 6) x 14 = 126
504 + 126 = 630
A function, f(x),represents the height of a plant x months after being planted. Students measure and record the height on a
Select the appropriate domain for this situation.
OA.
the set of all real numbers
OB.
the set of all integers
O c.
the set of all positive integers
OD
the set of all positive real numbers
Answer:
I think the answer would be A or B, the best would be B.
Step-by-step explanation:
K so since it is monthly, it would not be all positive data. So you are left with A or B. Integers are numbers that are positive and negative so since the data can be a range of positive and negative numbers, that is why the data set of all integers (b) is the best choice.
Your welcome :D
The J.R. Simplot Company produces frozen French fries that are then sold to customers such as McDonald's. The "prime" line of fries has an average length of 6.00 inches with a standard deviation of 0.50 inch. To make sure that Simplot continues to meet the quality standard for "prime" fries, they plan to select a random sample of n = 100 fries each day. The quality analysts will compute the mean length for the sample. They want to establish limits on either side of the 6.00 inch mean so that the chance of the sample mean falling within the limits is 0.99. What should these limits be?
Answer:
(5.871 `; 6.127)
Step-by-step explanation:
Given :
Mean = 6
Standard deviation. σ = 0.5
Samplr size, n = 100
Zcritical at 99% confidence = 2.58
The confidence interval :
Mean ± margin of error
Margin of Error = Zcritical * σ / sqrt(n)
Margin of Error = 2.58 * 0.5/sqrt(100) = 0.129
Confidence interval :
Lower boundary = 6.00 - 0.129 = 5.871
Upper boundary = 6.00 + 0.129 = 6.129
(5.871 `; 6.127)
1. A package of sticky notes is in the shape of
a parallelogram. The dimensions of one
sticky note are shown. What is the area of
one sticky note?
A. 248.4 cm?
B. 124.2 cm2
C. 62.1 cm2
D. 22.7 cm2
Answer:
B. 124.2
Step-by-step explanation:
Area= b*h
Area= 13.5*9.2
Area = 124.2
Please Note* = Multiply
9. What measure of central tendency is usually the preferred number by researchers for describing a group of scores?
10. Using the following data, calculate the standard deviation: 115, 125, 145, 150, 115, 125
The measure of central tendency that is usually the preferred number by researchers for describing a group of scores is the mean.
The measure of central tendency that is usually the preferred number by researchers for describing a group of scores is the mean. The mean provides the average score for a given set of data. It is calculated by summing up all the scores and dividing by the total number of scores. While other measures of central tendency, such as the median and mode, are also useful, the mean provides the most comprehensive picture of the data.
10. To calculate the standard deviation for the following data: 115, 125, 145, 150, 115, 125, you can use the following formula:
σ = √[(Σ(x - μ)²) / N]
Where:
σ = standard deviation
Σ = sum of
x = each score
μ = mean of all the scores
N = total number of scores
To find the standard deviation, first find the mean of the scores:
115 + 125 + 145 + 150 + 115 + 125 = 775
Total number of scores = 6
Mean = 775 / 6 = 129.17
Now, subtract the mean from each score, square the result, and add up all the squared differences:
(115 - 129.17)² + (125 - 129.17)² + (145 - 129.17)² + (150 - 129.17)² + (115 - 129.17)² + (125 - 129.17)² = 4666.79
Then, divide the sum of squared differences by the total number of scores and take the square root:
σ = √(4666.79 / 6) = 17.20
Mean = (115 + 125 + 145 + 150 + 115 + 125) / 6 = 129.17
Standard Deviation = √[ {(115 - 129.17)² + (125 - 129.17)² + (145 - 129.17)² + (150 - 129.17)² + (115 - 129.17)² + (125 - 129.17)² } / 6 ]
= √[4666.79 / 6]
= 17.20
Therefore, the standard deviation of the given data is 17.20.
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Prove the following:
(2cos x) / (cos 2x + 1) = sec x
The equation (2cos x) / (cos 2x + 1) = sec x is proven to be true.
We start with the expression on the left-hand side and simplify it step by step to show that it is equivalent to sec x.
(2cos x) / (cos 2x + 1) = (2cos x) / ((2cos^2 x - 1) + 1) [Using the double-angle formula cos 2x = 2cos^2 x - 1]
= (2cos x) / 2cos^2 x [Simplifying the numerator and denominator]
= cos x / cos^2 x [Cancelling out the factor of 2]
Now, we can simplify the expression further using the identity sec x = 1 / cos x:
cos x / cos^2 x = 1 / cos x = sec x.
Therefore, we have proved that (2cos x) / (cos 2x + 1) is equal to sec x.
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What is the volume of this sphere? Use a ~ 3.14 and round your answer to the nearest hundredth. 20 mm
Answer:
4186.67 cubic mm=V
Step-by-step explanation:
The volume of a sphere can be found using the equation, [tex]\frac{4}{3} \pi r^{3}[/tex]. It gives us the diameter but we need the radius. To find the radius just divde the diameter by 2, so the radius of the sphere is 10mm.
[tex]\frac{4}{3} (3.14) (10^{3})[/tex]=V
[tex]\frac{4}{3} (3.14) (1000)[/tex]=V
[tex]\frac{4}{3}[/tex](3140)=V
4186.67 cubic mm=V
8^x=1 Please solve for x.
Answer:
[tex] {8}^{x} = 1[/tex]
The exponent 0 makes the number as 1.
[tex]x = 0[/tex]
Answer:
the answer for x is = 0
Step-by-step explanation:
hope this helps
A right triangle has a 30° angle and the adjacent side to
the angle of length 6, draw the triangle and label all
sides and angles. Round to the nearest tenth.
Answer
let the triangle be supposed ABC
where angle BAC is 30 degree and angle ACB is 60 degree and where we know that angle ABC is right angled triangle which means angle ABC = 90 degree
the base side of triangle is 6cm which means ;
By taking angle A as reference angle
Hypotenuse = AC = x(let)
perpendicular = BC
base = AB = 6 cm
then by taking base and hypotenuse
b/h = AB/AC
or, cos (30 degree)= 6/ x
x =[tex]4\sqrt{x} 3[/tex] cm
that concluded that AC = [tex]4\sqrt{3}[/tex] cm
Now,
by phythagorous theorem,
[tex]h^{2} = p^{2} + b^{2}[/tex]
[tex]AC =\sqrt{AB^{2} + BC^{2} } AC = \sqrt{6^{2} + 4\sqrt{3} ^{2}} \\AC = 2\sqrt{21 } cm[/tex]
so, the length of side AB is 6 cm , BC is 4[tex]\sqrt{3}[/tex] cm and AC is 2[tex]\sqrt{21}[/tex] cm
Step-by-step explanation:
Simplify the following expressions to have fewer terms (MIDDLE SCHOOL)
5x-3+(4x-6)+2
4y+3-(8x-2)
Answer:
Install math calculator
Thank you
Answer:
x=1\9
Step-by-step explanation:
first part:
5x-3+4x+2
5x+4x-3+2
9x-1
9x=1
x=1\9 answer.
Please help.
Is algebra.
Answer:
1 is C
2 is B
3 is C
Step-by-step explanation:
Answer:
give em brainliest because i have no idea
Step-by-step explanation:
what are the answers to a, b, c, d?
Answer:
Step-by-step explanation:
(q11) Find the center of mass of the system of objects that have masses 2 , 3 and 5 at the point (-1,2),(1,1) and (3,3) respectively.
The center of mass of the system of objects that have masses 2 , 3 and 5 at the point (-1,2),(1,1) and (3,3) respectively is located at the point (1.6, 2.2).
To find the center of mass of the system of objects, we need to consider the masses and positions of each object. Let's go through the steps to calculate the center of mass:
Assign variables to the masses and coordinates of the objects:
Object 1: Mass = 2, Coordinates = (-1, 2)
Object 2: Mass = 3, Coordinates = (1, 1)
Object 3: Mass = 5, Coordinates = (3, 3)
Calculate the total mass of the system by summing the masses of the objects:
Total mass = 2 + 3 + 5 = 10
Calculate the weighted average of the x-coordinates and y-coordinates to find the center of mass:
Center of mass (x-coordinate) = (m1 * x1 + m2 * x2 + m3 * x3) / Total mass
Center of mass (y-coordinate) = (m1 * y1 + m2 * y2 + m3 * y3) / Total mass
Substituting the values:
Center of mass (x-coordinate) = (2 * -1 + 3 * 1 + 5 * 3) / 10 = ( -2 + 3 + 15) / 10 = 16 / 10 = 1.6
Center of mass (y-coordinate) = (2 * 2 + 3 * 1 + 5 * 3) / 10 = (4 + 3 + 15) / 10 = 22 / 10 = 2.2
Therefore, the center of mass of the system of objects is located at the point (1.6, 2.2).
The center of mass represents the average position of the system, taking into account the masses and positions of the objects. It is a point where the system can be considered to be balanced. Calculating the center of mass is important in various areas of physics, such as studying the motion, stability, and collisions of objects.
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