Consider two discrete random variables N_1 and N_2. The joint PMF is given by fn
ID: 3158404 • Letter: C
Question
Consider two discrete random variables N_1 and N_2. The joint PMF is given by fn_1, N_2 (n_1, n_2) = { C, n_2 = 0, 2, 4, 6, 8; n_1 = 0, 1,., n_2. 0, otherwise Find C for this to be a valid PMF. Find and sketch both CDFs F_N_1, (x) an F_N_2(x). Find the conditional PMFs f_N_2|N_1(n_2|n_1) and fn_1|n_2(n_1 | n_2). Determine whether N_1 and N_2 are independent. In the above problem 5.1. Find the mean, the 2nd order moment, the variance, and the 3rd order moment of N_1. Find the mean, the 2nd order moment, the variance, and the 3rd order moment of N_2. Find the correlation E{N_1 N_2}, the covariance, and the correlation coefficient of N_1 and N_2.Explanation / Answer
5.1 a) 10C = 1 implies C = 1/10
b) fn1 (x) = 5/10 = 1/2 n1 = 0,1
Fn1 (x) = 0 x<0
= 1/2 x=0
= 1 ;x >= 1
fn2 (x) = 2/10 if n2 = 0,2,4,6,8
Fn2(x) = 2/10 x = 0
= 4/10 x = 2
= 6/10 x=4
= 8/10 x=6
= 1 x>=8
f(n1,n2) = 1/10
f(n1) * f(n2) = 5/10*2/10 = 10/100 = 1/10 = f(n1,n2)
f(n2/n1) = [1/10 ] / 1/2 = 1/5
f(n1/n2) = [1/10] / 1/5 = 1/2