Question

Consider 3 trials, each having the same probability of success. Let X denote the total number of successes in these trials. If E[X]=1.8 what is the largest possible value of P{X=3}?

Answer 1

The answer is .6 and 0

Answer 2

Ok?

Answer 3

Use Chebishohv. inequality

Answer 4

P(abs(3-1.8)>=ksigma)<=1/k2

Answer 5

(1)P(1) + (2)P(2) + (3)P(3) = 1.8

If we let P(2) = 0, then (1)[1 - P(3)] + (3)P(3) = 1.8 will give P(3) = 0.4 which is the highest allowable for P(3)

Answer 6

Let me check P(1)=0
2(1-p)+3p=1.8
p<0 so P(2)=0 gives Maximum P.
Great