Autumn 2025 STAT 3450 Midterm 1
Practice Exam
Note: This practice is intended to give you a feel for the style of the exam. Working through
these problems is not, on its own, sufficient preparation for the midterm exam.
1. (3 points) For a binomial random variable with a small value of n and p<0.50, the
probability distribution of X will be:
a. Skewed to the right
b. Skewed to the left
c. Symmetric
d. Bimodal
e. Uniform
2. (3 points) Suppose P(B∣A)=0.30, P(B)=0.25, and P(A)=0.30. Based on these numbers,
we can conclude A and B are:
a. Both mutually exclusive and independent
b. Not mutually exclusive, but independent
c. Mutually exclusive and not independent
d. Not mutually exclusive and not independent
{0 ,∧otherwise
−x
3. (3 points) Consider the probability density function, f ( x ) =
e ,∧0< x <∞ . You can find
the mean of X by solving which mathematical expression?
∞
a. ∫ e
−x
dx
0
b. ∑ e
−x
x
∞
c. ∫ x e
−x
dx
0
d. ∑ x e
−x
x
∞
e. ∫ x e
2 −x
dx
0
f. ∑ x e
2 −x
x
4. (3 points) Let X be a random variable described by the function
{
2( x−1)
,∧1< x <4
f ( x )= 9 . Find P(X≥2).
0 ,∧otherwise
a. 0.111
Practice Exam
Note: This practice is intended to give you a feel for the style of the exam. Working through
these problems is not, on its own, sufficient preparation for the midterm exam.
1. (3 points) For a binomial random variable with a small value of n and p<0.50, the
probability distribution of X will be:
a. Skewed to the right
b. Skewed to the left
c. Symmetric
d. Bimodal
e. Uniform
2. (3 points) Suppose P(B∣A)=0.30, P(B)=0.25, and P(A)=0.30. Based on these numbers,
we can conclude A and B are:
a. Both mutually exclusive and independent
b. Not mutually exclusive, but independent
c. Mutually exclusive and not independent
d. Not mutually exclusive and not independent
{0 ,∧otherwise
−x
3. (3 points) Consider the probability density function, f ( x ) =
e ,∧0< x <∞ . You can find
the mean of X by solving which mathematical expression?
∞
a. ∫ e
−x
dx
0
b. ∑ e
−x
x
∞
c. ∫ x e
−x
dx
0
d. ∑ x e
−x
x
∞
e. ∫ x e
2 −x
dx
0
f. ∑ x e
2 −x
x
4. (3 points) Let X be a random variable described by the function
{
2( x−1)
,∧1< x <4
f ( x )= 9 . Find P(X≥2).
0 ,∧otherwise
a. 0.111
