can someone help me solve both a and b? Thanks.
can someone help me solve both a and b? Thanks. Problem 4 Let S and T...
5. Let the joint density of X and Y be fr(x,) = (x + y, fxy(x, y) = 0, 0<x< 1,0 <y <1 otherwise (a) Find the marginal pdfs of X and Y. (b) Are X and Y independent? (c) Are X and Y correlated? (d) Find P(X + Y < 1).
Solve #2, #3, and #4 1) Let X, Y be random variables with joint probability density function Find k and P(X 3, Y s 2). 2) For X,Y as in problem 1) find the marginal densitiesx(a) of X and fr (y) of Y. Are X, Y independent? Explain your answer. 3) For X, Y as in problem 1) find Cov(X, Y). 4) For X, Y as in problem 1) find the conditional probability
7. Two random variables X and Y have joint probability density function s(x, y) = $(1 – xy), 0<x< l; 0<y<l. The marginal pdfs for X and Y are respectively S(x) = {(2-x) 0<x< 1; s()= (2-y) 0<y<l. Determine the conditional expectation E(Y|X = x) and hence determine E(Y) [7] (ii) [3] Verify your answer to part (i) by calculating the value of E(Y) directly from the marginal pdf for Y. [Total 10]
6. Let g(t) = { 2te** t 20 6. Let g(t) be the probability density function of the continuous 0 t<0 random variable X. a. Verify that g(t) is indeed a probability density function. [8] b. Find the median of X, i.e. the number m such that P(x = m) = { = 0.5. [7]
1. Let X and Y be random variables with joint probability density function flora)-S 1 (2 - xy) for 0 < x < 1, and 0 <y <1 elsewhere Find the conditional probability P(x > ]\Y < ).
2. Let X and Y have joint density f(x.v) = \ şcy? if 0 <x< 1 and 1 <y<2, otherwise. (a) Compute the marginal probability density function of Y. If it's equal to 0 outside of some range, be sure to make this clear. (b) Set up but do not compute an integral to find P(Y < 2X).
5. Let X and Y have joint probability density function of the form Skxy if 0 < x +y < 1, x > 0 and y > 0, f(x,y)(, y) = { 0 otherwise. (a) What is the value of k? (b) Giving your reasons, state whether X and Y are dependent or independent. (c) Find the marginal probability density functions of X and Y. (d) Calculate E(X) and E(Y). (e) Calculate Cov(X,Y). (f) Find the conditional probability density function...
with steps pleas thanks 6. (20 Marks) If joint probability density function (pdliy of Xand is dehined S f(x, y) ={Cry a) Find C to have a valid joint density function x+ysi 0, Otherwise b) Find marginal pdfs of X and Y. (20 marks) Assume survival of transplanted hearts has an Exponential distribution with mean of 5 years. If a transplanted heart survives less than 4 years, the transplant is considered failure. Assume heart transplants are independent of each other,...
Can someone please help solve the problem below? I keep getting the answer incorrect. 12 (13 points) The random variables X and Y both have the same mean value of Their joint probability density function is (x+y, 0SX S1, 0 s y si fxy(x, y)= 0, otherwise. Determine the covariance of X and Y.
Can someone please help solve the problem below? I keep getting the answer incorrect. 12 (13 points) The random variables X and Y both have the same mean value of Their joint probability density function is (x+y, 0SX S1, 0 s y si fxy(x, y)= 0, otherwise. Determine the covariance of X and Y.