**18.1** The conditional distribution of *X* given that *Y = y* is

for *x* = 0, 1, 2,…, *y*. This is a binomial distribution with parameters *m = y* and *q* = *λ*_{1}/(*λ*_{1} + *λ*_{2}).

**18.2**

This is the hypergeometric distribution.

**18.3** Using (18.3) and conditioning on *N* yields

For the variance, use (18.6) to obtain

**18.4** (a) *f _{X}*(0) = 0.3,

*f _{Y}*(0) = 0.25,

(b) The following array presents the values for *x* = 0, 1, 2:

(c)

(d)

**18.5** (a)

Now a normal density *N*(*μ, σ*^{2}) has pdf . Then *f*_{X|Y}(*x*|*y*) ∝ *f*(*x, y*) is *N* .

(b)

Start Free Trial

No credit card required