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 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...
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...
Two components of a minicomputer have the following joint pdf for their useful lifetimesX and Y (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? x(1+y)dx = e-x for x 0 ye (1x)dy e for y 2 0 ye x(1+y)dx= for x 0 xe-x(1+y)dy-e* for x 2 0 for y e 0 What is the marginal pdf of Y?...
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...
ALL OF QUESTION 3 Question 3: Two components in a personal computer system have lifetimes (in years) that are distributed with a joint probability density function given by fx.Y(,y e-#(1+v), 0 < r,0 y, 0, otherwise (a) (3 marks). Find fx(x) (b) (3 marks). Find fy(y) (c) (3 marks). Find the probability that the lifetime of at least one com ponent exceeds 2 years. Question 4 Question 3: Two components in a personal computer system have lifetimes (in years) that...
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...
PROBLEM 1 Let the joint pdf of (X,Y) be f(x, y)= xe", 0<y<<< a. Compute P(X>Y). b. What is the conditional distribution of X given Y=y? Are X and Y independent? c. Find E(X|Y = y). d. Calculate cov(X,Y).
2. -30 a) The joint pdf of random variables X and Y is given by f(x,y) = 27ye-3 y<x<0, y >0. Show that the joint moment generating function(mgf) of X and Y is 27 M(t1, tz) = tı <3, tı + t, <3 (3 - tı) (3 - 7ı - t2) Use the joint mgf to obtain Cov(X,Y). b) Let X1, X2, X3 be independent random variables representing the lifetime of 3 electronic components with the following pdf, where X...