STAT 2857 Assignment 5
Problem 1. Let X have a geometric distribution with f (x) = p(1 p)x , x = 0, 1, 2, . . . Find the
probability function of R, the reminder when X is divided by 4.
Problem 2. The joint probability mass function of (X, Y ) is given by
STAT 2857 Formula Sheet for the Final Exam
For any numbers a1 , a2 , . . . , ar we have
(a1 + a2 + + ar )n =
(n1 ,n2 ,.,nr ) s.t.
n1 +n2 +nr =n
n1 0,.,nr 0
n!
an1 an2 anr .
r
n1 !n2 ! nr ! 1 2
Discrete uniform r.v. X cfw_1, 2, . . . , n, P (X = k ) = 1/
STAT 2857 Homework 1
Exercise 1. A survey of a groups viewing habits over the last year revealed the following information:
(i) 28% watched gymnastics
(ii) 29% watched baseball
(iii) 19% watched soccer
(iv) 14% watched gymnastics and baseball
(v) 12% watc
STAT 2857 Assignment 2
Problem 1. Let A, B and C be events such that Pcfw_A|C = 0.05 and Pcfw_B|C = 0.05. One of the
following statements must be true, which one?
A) Pcfw_A B|C = (0.05)2 B) Pcfw_Ac B c |C 0.90
C) Pcfw_A B|C 0.05
D) Pcfw_A B|C c 1 (0.05)2
STAT 2857 Assignment 3
Problem 1. Let X be a continuous non-negative random variable with density function f , and let
Y := X n . Find fY , the probability density function of Y .
Problem 2. A system consisting of one original unit plus a spare can functi
STAT 2857 Homework 1
Exercise 1. A survey of a groups viewing habits over the last year revealed the following information:
(i) 28% watched gymnastics
(ii) 29% watched baseball
(iii) 19% watched soccer
(iv) 14% watched gymnastics and baseball
(v) 12% watc
STAT 2857 Formula Sheet for the Final Exam
For any numbers a1 , a2 , . . . , ar we have
(a1 + a2 + + ar )n =
(n1 ,n2 ,.,nr ) s.t.
n1 +n2 +nr =n
n1 0,.,nr 0
n!
an1 an2 anr .
r
n1 !n2 ! nr ! 1 2
Discrete uniform r.v. X cfw_1, 2, . . . , n, P (X = k) = 1/n
STAT 2857 Assignment 4
Problem 1. a) Find the moments of the random variable X if its moment generating function is
MX (t) = (1 p1 p2 ) + p1 et + p2 e2t .
b) What is the variance of X?
Problem 2. Find the probability P (X 1.23) if X has moment generating