Mathematical Statistics 1 Exam 2
Modules 3 & 4 Fall 2026
MATH 4751/6751 Fall 2025
Instructions
Read and answer the following questions. Solutions presented without justification will receive
no credit. Round to four decimal places when the type of arithmetic is not specified.
Each question/page is worth the same number of points. Please circle the 3 questions (ques-
tion number or page number) that you want graded. Otherwise, I will only grade the first
3.
Graduate students are required to answer the graduate question. As well as 3 other questions
(please circle the corresponding page/question numbers).
1. At a carnival, you play a game where you draw 5 balls from a bag of 7 red and 3 green
balls. If you draw all 3 green balls, you win a Mimikyu plushie. The probability distribution
function for this game can be described as:
3 7
x 5−x
f (x) = for x = 0, 1, 2, 3
10
5
a. What is the probability you win the Mimikyu plushie on the first try?
b. What is the expected number of green balls a player will draw on any given attempt?
c. Describe and draw the cumulative probability distribution function for this distribu-
tion.
1
, 2. The following table describes a joint probability distribution of the random variables X
and Y :
y\x 0 1 2
12 15
0 0
60 60
6 20
1 0
60 60
3 4
2 0
60 60
a. Find P (X + Y < 2).
b. Find E[X].
c. Find E[Y ].
d. Find the covariance cov(X, Y ) and explain what it means.
2
Modules 3 & 4 Fall 2026
MATH 4751/6751 Fall 2025
Instructions
Read and answer the following questions. Solutions presented without justification will receive
no credit. Round to four decimal places when the type of arithmetic is not specified.
Each question/page is worth the same number of points. Please circle the 3 questions (ques-
tion number or page number) that you want graded. Otherwise, I will only grade the first
3.
Graduate students are required to answer the graduate question. As well as 3 other questions
(please circle the corresponding page/question numbers).
1. At a carnival, you play a game where you draw 5 balls from a bag of 7 red and 3 green
balls. If you draw all 3 green balls, you win a Mimikyu plushie. The probability distribution
function for this game can be described as:
3 7
x 5−x
f (x) = for x = 0, 1, 2, 3
10
5
a. What is the probability you win the Mimikyu plushie on the first try?
b. What is the expected number of green balls a player will draw on any given attempt?
c. Describe and draw the cumulative probability distribution function for this distribu-
tion.
1
, 2. The following table describes a joint probability distribution of the random variables X
and Y :
y\x 0 1 2
12 15
0 0
60 60
6 20
1 0
60 60
3 4
2 0
60 60
a. Find P (X + Y < 2).
b. Find E[X].
c. Find E[Y ].
d. Find the covariance cov(X, Y ) and explain what it means.
2
