Statistical Inference I: J. Lee
Assignment 1
Problem 1. An exam has 10 multiple choice questions where each question has 5 possible answers.
(a) If student goes into exam completely unprepared and guesses on all 10, what is the probability of
getting at l
Statistical Inference I: J. Lee
Assignment 6 Solution Notes
Problem 1.
(a)
(i) We find c by setting
Z
Z
Z
y
Z
c(y 2 x2 )ey dxdy = 8c,
f (x, y)dxdy =
1=
y
0
so c R= 1/8.
(You need not evaluate the integral; it is OK to just ay that c = 1/A, where
Ry
A = 0
Statistical Inference I: J. Lee
Assignment 7 Solution Notes
Problem 1.
(a) The marginal density, fY (y), of Y is given by
0
Z
R 4 Cx2 dx = (C/3)(64 + y 3 )
Ry
f (x, y)dx =
fY (y) =
4
Cx2 dx = (C/3)(64 y 3 /8)
y/2
0
if y < 4
if 4 < y < 0
if 0 < y < 8
if
Statistical Inference I: J. Lee
Assignment 5
Problem 1. Two fair dice are rolled. Find the joint probability mass function of X and Y , where X is the
largest value obtained on any die, and Y is the sum of the values on the two dice.
Problem 2. Suppose th
Statistical Inference I: J. Lee
Assignment 5 Solution Notes
Problem 1. Let X be the larger of the two values, and let Y be the sum of the two values. Then,
X cfw_1, 2, . . . , 6 and Y cfw_2, 3, . . . , 12.
p(1, 2) = P (X = 1, Y = 2) = P (cfw_(1, 1)) = 1/3
Statistical Inference I: J. Lee
Assignment 6
Problem 1. SELECT ONE OF THE FOLLOWING THREE PROBLEMS TO DO AND TURN IN.
You should understand how to do all three, since they provide good practice.
(a) Let X and Y have joint density
f (x, y) =
c(y 2 x2 )ey
0
Statistical Inference I: J. Lee
Assignment 2
Problem 1. In your pocket, you have 1 dime, 2 nickels, and 2 pennies. You select 2 coins at random
(without replacement). Let X represent the amount (in cents) that you select from your pocket.
(a) Give (explic
Statistical Inference I: J. Lee
Assignment 1 Solution Notes
Problem 1. Solved in class.
Problem 2.
(a) either A or B occurs; P (A B) = P (A) + P (B) P (A B) = 0.35 + 0.51 0 = 0.86.
(b) A occurs but B does not; P (A B c ) = P (A) = 0.35, since A B c .
(c)
Statistical Inference I: J. Lee
Assignment 2 Solution Notes
Problem 1.
(a) By considering each possible outcome, we see that the possible
probability function is given by
2
(2)
= 0.1
(52)
(21)(21)
= 0.4
(52)
(2)
25 = 0.1
(2)
p(x) = P (X = x) =
1 2
(1)