Math 303
Day 17 Worksheet Name:
The goal of this worksheet is to help you become more familiar with our examples of discrete
random variables. Below is a list of our examples and their relevant properties. Do what you can in
class today and what you don’t finish is homework. This worksheet is due Wednesday 2/27
•(4.6) Binomial:
–parameters (n, q)
–takes values 0,1,2,. . . , n
–p(i) = n
iqi(1 −q)n−i
–E[X] = nq and V ar(X) = nq(1 −q)
–Bernoulli r.v. is a binomial r.v. with n= 1
•(4.8.2) Negative Binomial:
–parameters (r, q)
–takes values r, r + 1, r + 2, . . .
–p(n) = n−1
r−1qr(1 −q)n−r
–E[X] = r
qand V ar(X) = r(1−q)
q2
–Geometric r.v. is a negative binomial r.v. with r= 1
•(4.8.3) Hypergeometric:
–parameters (n, N, m)
–takes values 0,1,2,...,min{n,m}
–p(i) = (m
i)(N−m
n−i)
(N
n)
–Let q=m
Nthen E[X] = nq and V ar(X) = nq(1 −q)1−n−1
N−1
•(4.7) Poisson:
–parameter λ
–takes values 0,1,2,. . .
–p(i) = e−λλi
i!
–E[X] = V ar(X) = λ
(1) A company produces fine crystal and from experience they know that 10% of their goblets
have cosmetic flaws that require them to be considered “seconds”.
(a) What type of random variable are you going to use and what are the parameters?
(b) Among six randomly selected goblets what is the probability that exactly one is a
second?
(c) Among six randomly selected goblets what is the probability that at least one is a
second?
(d) Among six goblets how many should they expect to be seconds?
(2) A store receives a shipment of 15 digital cameras. There are six 7-megapixel cameras and
the rest are 10-megapixel cameras. Five of these cameras are to be randomly selected to
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