Exercise 3.34

Answers

(a)

Let

Y

be the number of Statistics students in the sample of size

m

P (Y = k) = \sum_{i = k}^{n} P (X = i) P (Y = k | X = i) = \sum_{i = k}^{n} (\binom{n}{i}) p^{i} {(1 - p)}^{n - i} \frac{(\binom{i}{k}) (\binom{n - i}{m - k})}{(\binom{n}{m})}

(b)

Consider a student in a random sample of size

m

. Independently of other students, the student has probability

p

of being a statistics major. Then, the probability of

k

students in the sample being statistics majors is

(\binom{m}{k}) p^{k} {(1 - p)}^{m - k}

. Thus,

Y \sim Binom (m, p)

fifthist

2021-12-05 00:00