3. Suppose X, Y are discrete random variables taking values in {-1,0,1) and their joint probability...
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
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
The joint probability mass function of two discrete random variables A and B is (i) Are A and B are uncorrelated? (ii) Are A and B independent? Sca²b, a=-2,2 and b = 1,2 PA,(a,b) = 0, otherwise
20. (8 points) Suppose X, Y, and Z are discrete random variables with joint probability mass function P(x, y, z) given below. Be sure to full justify your answers and show ALL work. P(0,0,0) = 2,3 P(0,0,1) 33 P(0,1,0) = P(1,0,0) = 32 P(1,0,1) = P(1,1,0) = 32 a. Find the marginal probability mass function for 2, pz(2). b. What is E[X | Y = 0]? P(0,1,1) = 4 P(1,1, 1) = 32
[1] The joint probability mass function of two discrete random variables A and B is PAB(a, b) = Sca²b, a = -2,2 and b = 1,2 0, otherwise Clearly stating your reasons, answer the following two (i) Are A and B are uncorrelated? (ii) Are A and B independent? [2] X is continuous uniform (1,7) while Y is exponential with mean 2. If the variance of (X+2Y) is 20, find the correlation coefficient of X and Y.
[1] The joint probability mass function of two discrete random variables A and B is 0, Pab(a,b) = Sca²b, a = -2, 2 and b = 1,2 otherwise Clearly stating your reasons, answer the following two (i) Are A and B are uncorrelated? (ii) Are A and B independent?
The discrete random variables X and Y take integer values with joint probability distribution given by f (x,y) = a(y−x+1) 0 ≤ x ≤ y ≤ 2 or =0 otherwise, where a is a constant. 1 Tabulate the distribution and show that a = 0.1. 2 Find the marginal distributions of X and Y. 3 Calculate Cov(X,Y). 4 State, giving a reason, whether X and Y are independent. 5 Calculate E(Y|X = 1).
Problem 5 Define X and Y to be two discrete random variables whose joint probability mass function is given as follows: e-127m5n-m P(X = m, Y = n) = m!(n - m)! for m <n, m> 0 and n > 0, while P(X = m, Y = n) = 0 for other values of m, n 1. Calculate the probability that 1 < X <3 and 0 <Y < 2. 2. Calculate the marginal probability mass functions for the random...
[1] The joint probability mass function of two discrete random variables A and B is Pab(a,b) = {ca2b, a = -2,2 and b = 1,2 otherwise Clearly stating your reasons, answer the following two (1) Are A and B are uncorrelated? (ii) Are A and B independent? [2] X is continuous uniform (1,7) while Y is exponential with mean 2. If the variance of (X+2Y) is 20, find the correlation coefficient of X and Y.
[1] The joint probability mass function of two discrete random variables A and B is Pab(a,b) = {ca?b, Sca²b, a= -2,2 and b = 1,2 otherwise Clearly stating your reasons, answer the following two (i) Are A and B are uncorrelated? (ii) Are A and B independent?