The joint probability function of two discrete r.v's X and Y is given by f(x, y) = c(2x+y), where x and y can assume all integers such that 0≤x≤2,0≤y≤3 and f(x,y) =0 otherwise. Find E(X), E(Y) , E(XY), E(X2), E(Y2), var(X), var(Y), cov(X, Y) and ρ.

**Mumbai University > Electronics and Telecommunication Engineering > Sem 5 > Random Signal Analysis

Marks: 10M

Year: May 2016

X and Y are discrete RVs

To find c:

We can tabulate the probabilities as follows:

f(x,y)= c(2x+y) ........ 0≤x≤2,0≤y≤3

=0

Since ∑$p_i$=1

∴42c=1

∴c=1/42

With this value the probability distribution is

∴The marginal probability distributions of X & Y are: