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Two components of a minicomputer have the following joint pdf for their useful lifetimesX and Y...
Two components of a minicomputer have the following joint pdf for their useful lifetimes X and...
Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: FY 1 xe A1 + + x2 0 and v2 0 1 0 otherwise (a) What is the probability that the lifetime X of the first component exceeds 4? (Round your answer to three decimal places.) (b) What is the marginal pdf of X? xe X(1+y)dy = e X for x 2 0 dx = 1 (1 + vi for y xe X(1+y)dx...
Problem 4: Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: xe-(+) ;x&...
Problem 4: Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: xe-(+) ;x>0;y>0 0 ; elsewhere fx y(x,y)- (a) Explain whether the lifetimes of two components are independent based on probability. (b) Compute the probability that the lifetime (X) exceeds 3.5 (c) Compute the probability that the lifetime of at least one component exceeds 3.5. (d) Compute the marginal pdf of X
Problem 4: Two components of a minicomputer have the following...
Problem 4: Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: xe-(+) ;x&...
Problem 4: Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: xe-(+) ;x>0;y>0 0 ; elsewhere fx y(x,y)- (a) Explain whether the lifetimes of two components are independent based on probability. (b) Compute the probability that the lifetime (X) exceeds 3.5 (c) Compute the probability that the lifetime of at least one component exceeds 3.5. (d) Compute the marginal pdf of X
Problem 4: Two components of a minicomputer have the following...
Two components of a minicomputer have the following joint pdf for their useful lifetimes X and...
Two components of a minicomputer have the following
joint pdf for their useful lifetimes X and Y:
f (x, y) 5 5xe2x(11y) x $ 0 and y $ 0
0 otherwise
a. What is the probability that the lifetime X of the first
component exceeds 3?
b. What are the marginal pdf’s of X and Y? Are the two
lifetimes independent? Explain.
c. What is the probability that the lifetime of at least
one component exceeds 3?
12. Two components...
I have solved all the questions except part C. Two components of a minicomputer have the...
I have solved all the questions except part C.
Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: x, y)xe-xx 2 0 and y 2 0 0 otherwise (a) What is the probability that the lifetime X of the first component exceeds 2? (Round your answer to three decimal places.) 135 (b) What is the marginal pdf of X? o ye 2 for x 2 0 (1 +x2 for x2 o
Q6. The lifetimes of two components in a machine have the following joint pdf: f(x, y).00-x...
Q6. The lifetimes of two components in a machine have the following joint pdf: f(x, y).00-x y) for 0<50-y < 50 and zero elsewhere a. What is the probability that both components are functioning 20 months from now. b. What is the probability the component with life time X would fail 3 months before the other one? c. Compute the covariance of X, Y d. Compute the expected life of the machine e. What is probability that the two components...
4. Two random variables X and Y have the following joint probability density function (PDF) Skx 0<x<y<1, fxy(x...
4. Two random variables X and Y have the following joint probability density function (PDF) Skx 0<x<y<1, fxy(x, y) = 10 otherwise. (a) [2 points) Determine the constant k. (b) (4 points) Find the marginal PDFs fx(2) and fy(y). Are X and Y independent? (c) [4 points) Find the expected values E[X] and EY). (d) [6 points) Find the variances Var[X] and Var[Y]. (e) [4 points) What is the covariance between X and Y?
Suppose X and Y have the joint pdf f (x, y) = 3y, 0 < y...
Suppose X and Y have the joint pdf f (x, y) = 3y, 0 < y < 1, y − 1 < x < 1 − y 0 otherwise a) Give an expression for P (X > Y ). b) Find the marginal pdfs for Y . c) Find the conditional pdf of X given Y = y, where 0 < y < 1. d) Give an expression for E[XY ]. e) Are X and Y independent?
need help for a and c. Thank you! Two components of a laptop computer have the...
need help for a and c. Thank you!
Two components of a laptop computer have the following joint probability density function for their useful lifetimes X and Y (in years): f(x,y) = a. Find the marginal probability density function of X, fx(x). Enter a formula below. Use for multiplication, / for division, A for power and exp for exponential function. For example, otherwise 3*xA3 exp(-x/3) means 3x3e3 X 2 0 Submit Answer Incorrect. Tries 3/10 Previous Tries b. Find the...
1. The joint probability density function (pdf) of X and Y is given by fxy(x, y)...
1. The joint probability density function (pdf) of X and Y is given by fxy(x, y) = A (1 – xey, 0<x<1,0 < y < 0 (a) Find the constant A. (b) Find the marginal pdfs of X and Y. (c) Find E(X) and E(Y). (d) Find E(XY). 2. Let X denote the number of times (1, 2, or 3 times) a certain machine malfunctions on any given day. Let Y denote the number of times (1, 2, or 3...
Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: FY 1 xe A1 + + x2 0 and v2 0 1 0 otherwise (a) What is the probability that the lifetime X of the first component exceeds 4? (Round your answer to three decimal places.) (b) What is the marginal pdf of X? xe X(1+y)dy = e X for x 2 0 dx = 1 (1 + vi for y xe X(1+y)dx...
Problem 4: Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: xe-(+) ;x>0;y>0 0 ; elsewhere fx y(x,y)- (a) Explain whether the lifetimes of two components are independent based on probability. (b) Compute the probability that the lifetime (X) exceeds 3.5 (c) Compute the probability that the lifetime of at least one component exceeds 3.5. (d) Compute the marginal pdf of X
Problem 4: Two components of a minicomputer have the following...
Problem 4: Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: xe-(+) ;x>0;y>0 0 ; elsewhere fx y(x,y)- (a) Explain whether the lifetimes of two components are independent based on probability. (b) Compute the probability that the lifetime (X) exceeds 3.5 (c) Compute the probability that the lifetime of at least one component exceeds 3.5. (d) Compute the marginal pdf of X
Problem 4: Two components of a minicomputer have the following...
Two components of a minicomputer have the following
joint pdf for their useful lifetimes X and Y:
f (x, y) 5 5xe2x(11y) x $ 0 and y $ 0
0 otherwise
a. What is the probability that the lifetime X of the first
component exceeds 3?
b. What are the marginal pdf’s of X and Y? Are the two
lifetimes independent? Explain.
c. What is the probability that the lifetime of at least
one component exceeds 3?
12. Two components...
I have solved all the questions except part C.
Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: x, y)xe-xx 2 0 and y 2 0 0 otherwise (a) What is the probability that the lifetime X of the first component exceeds 2? (Round your answer to three decimal places.) 135 (b) What is the marginal pdf of X? o ye 2 for x 2 0 (1 +x2 for x2 o
Q6. The lifetimes of two components in a machine have the following joint pdf: f(x, y).00-x y) for 0<50-y < 50 and zero elsewhere a. What is the probability that both components are functioning 20 months from now. b. What is the probability the component with life time X would fail 3 months before the other one? c. Compute the covariance of X, Y d. Compute the expected life of the machine e. What is probability that the two components...
4. Two random variables X and Y have the following joint probability density function (PDF) Skx 0<x<y<1, fxy(x, y) = 10 otherwise. (a) [2 points) Determine the constant k. (b) (4 points) Find the marginal PDFs fx(2) and fy(y). Are X and Y independent? (c) [4 points) Find the expected values E[X] and EY). (d) [6 points) Find the variances Var[X] and Var[Y]. (e) [4 points) What is the covariance between X and Y?
need help for a and c. Thank you!
Two components of a laptop computer have the following joint probability density function for their useful lifetimes X and Y (in years): f(x,y) = a. Find the marginal probability density function of X, fx(x). Enter a formula below. Use for multiplication, / for division, A for power and exp for exponential function. For example, otherwise 3*xA3 exp(-x/3) means 3x3e3 X 2 0 Submit Answer Incorrect. Tries 3/10 Previous Tries b. Find the...
1. The joint probability density function (pdf) of X and Y is given by fxy(x, y) = A (1 – xey, 0<x<1,0 < y < 0 (a) Find the constant A. (b) Find the marginal pdfs of X and Y. (c) Find E(X) and E(Y). (d) Find E(XY). 2. Let X denote the number of times (1, 2, or 3 times) a certain machine malfunctions on any given day. Let Y denote the number of times (1, 2, or 3...
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