Contrast the Poisson guess and the right binomial likelihood for the accompanying cases: (a) P{X = 2} when n = 8, p = 0.1.

(b) P{X = 9} when n = 10, p = 0.95.

(c) P{X = 0} when n = 10, p = 0.1.

(d) P{X = 4} when n = 9, p = 0.2.

14))

A urn contains n + m balls, of which n are red and m are dark. They are removed from the urn, each in turn and without substitution. Leave X alone the quantity of red balls eliminated before the main torpedo is picked. We are keen on deciding E(X). To acquire this amount, number the red balls from 1 to n. Presently characterize the irregular factors Xi = 1, ... by

Xr 1, if red ball I is taken before any repudiate is picked = 0, in any case

(a) Express X as far as the Xi.

(b) Find E(X).

15))

It Xis a nonnegative whole number esteemed arbitrary variable, snow that

11=0

Clue: Define the grouping ot arbitrary factors In, n 1, by

ifnsX

1,

O, ifn>X

Presently express X as far as the \

(b) It X and Yare both nonnegative whole number esteemed irregular factors, snow that

E[XYI = n, Y m)

16))

Think about three preliminaries, each ot which is either a triumph or not. Allow X to signify the number ot

triumphs. Assume that E(X) = 1.8.

(a) What is the biggest conceivable worth of PIX= 3}?

(b) What is the littlest conceivable worth of 3}?

In the two cases, build a likelihood situation that outcomes in P{X

3} having the ideal worth.