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Consider 3 trials, each having the same probability of successes. Let X denote the total number of successes in these trials.


If E(X) = 1.8, determine:

Athe largest possible value of P{X=3}?
Bthe smallest possible value of P{X=3}?

In both cases, construct a probability scenario that results in P{X=3} having the stated value.

Verified Answer :

meerkat18

Since each trial has the same probability of success, 

Let, Xi=1 if the ith trial is a success (0 otherwise). Then, X=∑3i=1XiX=∑i=13Xi, 

and E[X]=E[∑3i=1Xi]=∑3i=1E[Xi]=∑3i=1p=3p=1.8E[X]=E[∑i=13Xi]=∑i=13E[Xi]=∑i=13p=3p=1.8

So, p=0.6p=0.6, and P{X=3}=0.63P{X=3}=0.63

I thought what I did was sound, but the textbook says the answer to (a) is 0.60.6 and (b) is 00.

Their reasoning (for (a)) is as follows:

View image meerkat18

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