Chapter 5.1, Problem 2E

a.

To determine

Find the value of c that makes the function $f\left(x,y\right)=c\left(x+y\right)$ a joint probability mass function over the nine points with $x=1,2,3$ and $y=1,2,3$.

Compute $P\left(X=1,Y<4\right)$.

b.

To determine

Compute $P\left(X=1\right)$.

c.

To determine

Compute $P\left(Y=2\right)$.

d.

To determine

Compute $P\left(X<2,Y<2\right)$.

e.

To determine

Compute $E\left(X\right)$, $E\left(Y\right)$, $V\left(X\right)$ and $V\left(Y\right)$.

f.

To determine

Find marginal probability distribution of X.

g.

To determine

Find the conditional probability distribution of Y given that $X=1$.

h.

To determine

Find the conditional probability distribution of X given that $Y=2$.

i.

To determine

Find $E\left(Y|X=1\right)$.

j.

To determine

Explain whether X and Y are independent or not.