Review Problem, 4-R2 in Berry & Lindgren - Statistics: Theory & Methods

Let X ~ Ber(.04). If this experiment is repeated in independent trials.

(a) how many trials, on average, would be required to get six successes?

Let X1 denote the number of successes in 50 trials and X2, the number of successes in 50 additional trials. Let Y = X1 + X2.

(b) Find the mean and variance of Y.

(c) Give the distribution of Y (name and parameter value)

(d) Find P(Y<=5) (that's Y equal to or smaller than 5)

(e) Find the probability that if there are six successes in the 100 trials, these are evenly divided between the first 50 and the second 50 trials.

That's it.

Any help is sincerely appreciated.

Thanks, Simon DK.