,MATH 110 Module 4 | Practice Q&A | 2026/2027 | Statistics | Portage
Learning | 100% PASS
1. A random variable that can take on any value within a given range is
called a:
A) Discrete random variable
B) Continuous random variable
C) Binomial random variable
D) Poisson random variable
Correct Answer: Continuous random variable
Rationale: A continuous random variable can take on any value within a
given range (e.g., height, weight, temperature). A discrete random variable
takes on specific, distinct values (e.g., number of heads in coin tosses).
2. A random variable that can only take on specific, distinct values is called
a:
A) Continuous random variable
B) Discrete random variable
C) Normal random variable
D) Uniform random variable
Correct Answer: Discrete random variable
Rationale: A discrete random variable takes on specific, distinct values, often
whole numbers (e.g., number of defective items, number of successes in
binomial experiments). Continuous variables can take any value in an
interval.
,3. The expected value of a discrete random variable is calculated as:
A) Σ[x² × P(x)]
B) Σ[x × P(x)]
C) Σ[P(x)]
D) Σ[x]
Correct Answer: Σ[x × P(x)]
Rationale: The expected value (mean) of a discrete random variable is the
sum of each value multiplied by its probability: E(X) = Σ[x × P(x)]. This
represents the long-run average of the random variable.
4. The variance of a discrete random variable is calculated as:
A) Σ[x × P(x)]
B) Σ[(x - μ)² × P(x)]
C) Σ[(x - μ) × P(x)]
D) Σ[x² × P(x)]
Correct Answer: Σ[(x - μ)² × P(x)]
Rationale: The variance of a discrete random variable is the sum of the
squared deviations from the mean, each weighted by its probability: Var(X) =
Σ[(x - μ)² × P(x)]. The standard deviation is the square root of the variance.
5. Which of the following is NOT a condition for a binomial experiment?
A) Fixed number of trials
B) Each trial has two possible outcomes (success/failure)
C) The probability of success changes from trial to trial
, D) The trials are independent
Correct Answer: The probability of success changes from trial to trial
Rationale: A binomial experiment requires a fixed number of trials, two
possible outcomes (success/failure), a constant probability of success (p) for
each trial, and independent trials. The probability of success must remain
constant.
6. In a binomial experiment, the probability of failure is denoted by:
A) p
B) 1 - p
C) q
D) Both B and C
Correct Answer: Both B and C
Rationale: In a binomial experiment, the probability of failure is denoted by q
= 1 - p. Both "1 - p" and "q" are correct notations for the probability of
failure.
7. The binomial probability formula is:
A) P(X = x) = C(n,x) × p^x × (1-p)^(n-x)
B) P(X = x) = C(n,x) × p^(n-x) × (1-p)^x
C) P(X = x) = C(n,x) × p^x × (1-p)^x
D) P(X = x) = n! / x!
Correct Answer: P(X = x) = C(n,x) × p^x × (1-p)^(n-x)
Learning | 100% PASS
1. A random variable that can take on any value within a given range is
called a:
A) Discrete random variable
B) Continuous random variable
C) Binomial random variable
D) Poisson random variable
Correct Answer: Continuous random variable
Rationale: A continuous random variable can take on any value within a
given range (e.g., height, weight, temperature). A discrete random variable
takes on specific, distinct values (e.g., number of heads in coin tosses).
2. A random variable that can only take on specific, distinct values is called
a:
A) Continuous random variable
B) Discrete random variable
C) Normal random variable
D) Uniform random variable
Correct Answer: Discrete random variable
Rationale: A discrete random variable takes on specific, distinct values, often
whole numbers (e.g., number of defective items, number of successes in
binomial experiments). Continuous variables can take any value in an
interval.
,3. The expected value of a discrete random variable is calculated as:
A) Σ[x² × P(x)]
B) Σ[x × P(x)]
C) Σ[P(x)]
D) Σ[x]
Correct Answer: Σ[x × P(x)]
Rationale: The expected value (mean) of a discrete random variable is the
sum of each value multiplied by its probability: E(X) = Σ[x × P(x)]. This
represents the long-run average of the random variable.
4. The variance of a discrete random variable is calculated as:
A) Σ[x × P(x)]
B) Σ[(x - μ)² × P(x)]
C) Σ[(x - μ) × P(x)]
D) Σ[x² × P(x)]
Correct Answer: Σ[(x - μ)² × P(x)]
Rationale: The variance of a discrete random variable is the sum of the
squared deviations from the mean, each weighted by its probability: Var(X) =
Σ[(x - μ)² × P(x)]. The standard deviation is the square root of the variance.
5. Which of the following is NOT a condition for a binomial experiment?
A) Fixed number of trials
B) Each trial has two possible outcomes (success/failure)
C) The probability of success changes from trial to trial
, D) The trials are independent
Correct Answer: The probability of success changes from trial to trial
Rationale: A binomial experiment requires a fixed number of trials, two
possible outcomes (success/failure), a constant probability of success (p) for
each trial, and independent trials. The probability of success must remain
constant.
6. In a binomial experiment, the probability of failure is denoted by:
A) p
B) 1 - p
C) q
D) Both B and C
Correct Answer: Both B and C
Rationale: In a binomial experiment, the probability of failure is denoted by q
= 1 - p. Both "1 - p" and "q" are correct notations for the probability of
failure.
7. The binomial probability formula is:
A) P(X = x) = C(n,x) × p^x × (1-p)^(n-x)
B) P(X = x) = C(n,x) × p^(n-x) × (1-p)^x
C) P(X = x) = C(n,x) × p^x × (1-p)^x
D) P(X = x) = n! / x!
Correct Answer: P(X = x) = C(n,x) × p^x × (1-p)^(n-x)
