The shooter

The shooter shoots at the target, assuming that the individual shots are independent of each other and the probability of hitting each of them is 0.2. The shooter fires until he hits the target for the first time, then stop firing.
(a) What is the most likely number of shots?
(b) What an average number of shots do you expect?
(c) What is the variance of the number of shots?

Correct result:

a =  4.48


c(n,1)=n  p(n)=n 0.8(n1) 0.2=0  maxp(4.48)=0.4216  a=4.48=11225

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