1. The joint PDF of two random variables are given in the following table a) (0.3...
Suppose X, Y are random variables whose joint PDF is given by . 1 0 < y < 1,0 < x < y y otherwise 0, 1. Find the covariance of X and Y. 2. Compute Var(X) and Var(Y). 3. Calculate p(X,Y).
you have two random variables, X and Y with joint distribution given by the following table: Y=0 | .4 .2 4+.26. So, for example, the probability that Y 0, X - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),f(r). (b) Find the conditional distribution (pmf) of Y give X, denoted f(Y|X). (c) Find the expected values of X and Y, E(X), E(Y). (d) Find the variances of X...
2. The joint pdf of random variables X and Y is given by f(x.y) k if 0 sysxs2 and f(x,y)-0 otherwise. a. Find the value of k b. Find the marginal pdfs of X and Y. Are X and Y independent? c. Find Covariance (X,Y) and Correlation(X,Y). Why cannot we say that X and Y have linear relation Yea X+ b, where a and b are real numbers?
3. Suppose the joint PDF of two random variables X and Y are given below 3(xy2 + x2y), if o sxs 1,0 Sy s 1, fx.x (x,y) otherwise. (1) What is the covariance of X and Y? (20 points) (2) What is the correlation between X and Y? (20 points) 0,
Q2) (20 points) The joint pdf of a two continuous random variables is given as follows: < x < 2,0 < y<1 (cxy0 fxy(x, y) = } ( 0 otherwise 1) Find c. 2) Find the marginal PDFs of X and Y. Make sure to write the ranges. Are these random variables independent? 3) Find P(0 < X < 110 <Y < 1) 4) What is fxy(x\y). Make sure to write the range of X.
5. Suppose that the joint pdf of the random variables X and Y is given by - { ° 0 1, 0< y < 1 f (x, y) 0 elsewhere a) Find the marginal pdf of X Include the support b) Are X and Y independent? Explain c) Find P(XY < 1)
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...
The joint pdf of random variables X and Y is given by f(x.y)-k if 0 s y sx s 2 and f(x,y) =0 otherwise. a. Find the value of k b. Find the marginal pdfs of X and Y. Are X and Y independent? c. Find Covariance (X,Y) and Correlation(X,Y). Why cannot we say that X and Y have linear relation Y-a X+ b, where a and b are real numbers?
Let X and Y be continuous random variables with joint pdf fx.v (x, y)-3x, OSysx<1, and zero otherwise. a. b. c. d. e. What is the marginal pdf of X? What is the marginal pdf of Y? What is the expectation of X alone? What is the covariance of X and Y? What is the correlation of X and Y?
The joint PDF of random variables X and Y is expressed as
(a) Determine the constant c.
(b) Determine the marginal density function for X.
(c) Determine the marginal density function for Y.
(d) Are X and Y statistically independent?
(e) Determine the probability of P(X ≤ 0.5 | Y = 1).
The joint PDF of random variables X and Y is expressed as certy, 05xs1 and 05ys2 fx.x(x, y) = 10. elsewhere. (a) Determine the constant c. (b) Determine...