Please select 2 & 3 2. Let X and Y be discrete random variables taking values...
please help me! 3. Suppose X, Y are discrete random variables taking values in-1,0, 1) and their joint probability mass function is 0 0 X=1 where a, b are two positive real numbers (i) Find the values of a and b such that X and Y are uncorrelated (ii) Show that X and Y cannot be independent. 0
3. Suppose X, Y are discrete random variables taking values in -1,0,1) and their joint probability mass function is 0 0 0 where a, b are two positive real numbers. (i) Find the values of a and b such that X and Y are uncorrelated (ii) Show that X and Y cannot be independent
3. Suppose X, Y are discrete random variables taking values in {-1,0,1) and their joint probability mass function is 0 X=1 where a, b are two positive real numbers. (i) Find the values of a and b such that X and Y are uncorrelated. (ii) Show that X and Y cannot be independent 0
Let X and Y be a random variables taking values 1,2, and 3 with joint I/ 01/8 나.rapis. |probabilitiespxY (1, J) given by the matrix shown: 0 1/2 0 1/8 0 1/8 4 pt. Calculate and sketch joint CDF Fxy(i,j). Find px (i) and pr(i) for ii12, 3. Compute P(X2Y). 3 pt
Problem 3. Let X and Y be two independent random variables taking nonnegative integer values (a) Prove that for any nonnegative integer m 7m k=0 b) Suppose that X~ B (n, p) and Y ~ B(m. p), and X, Y are independent. What is the distribution of the random variable Z X + Y? (c) Prove the following formula for binomial coefficients: n\ _n + m for kmin (m, n) (d) Let X ~ B (n, 1/2). What is P...
Let X and Y be two discrete random independent random variables. p(x) = 1/3 for x =-2,-1,0 p(y) = 1/2 for y =1,6 K = X + Y
Let X and Y be two discrete random independent random variables. p(x) = 1/3 for x =-2,-1,0 p(y) = 1/2 for y =1,6 Z = X + Y. What is the distribution of Z using the method of MGF's
Problem 4 Let X be the following discrete random variable: Let Y = X2. Show that cov(X·Y) = 0, but X and Y are not independent random variable.
2. Let X and Y be two independent discrete random variables with the probability mass functions PX- = i) = (e-1)e-i and P(Y = j-11' for i,j = 1, 2, Let {Uni2 1} of i.i.d. uniform random variables on [0, 1]. Assume the sequence {U i independent of X and Y. Define M-max(UhUn Ud. Find the distribution
1. Let X and Y have a discrete joint distribution with ( P(X = x, Y = y) = {1, 10, if (x, y) = (-1,1) if x = y = 0 elsewhere Show that X and Y are uncorrelated but not independent. [5 points] 2. Let X and Y have a discrete joint distribution with f(-1,0) = 0, f(-1,1) = 1/4, f(0,0) = 1/6, f(0, 1) = 0, $(1,0) = 1/12, f(1,1) = 1/2. Show that (a) the two...