250+ TOP MCQs on Gamma Distribution and Answers

Probability and Statistics Multiple Choice Questions & Answers (MCQs) on “Gamma Distribution”.

1. The mean and the variance for gamma distribution are __________
a) E(X) = 1/λ, Var(X) = α/λ²
b) E(X) = α/λ, Var(X) = 1/λ²
c) E(X) = α/λ, Var(X) = α/λ²
d) E(X) = αλ, Var(X) = αλ²
Answer: c
Clarification: The mean and the variance for gamma distribution is given as
E(X) = α/λ, Var(X) = 1/λ².

2. Putting α=1 in Gamma distribution results in _______
a) Exponential Distribution
b) Normal Distribution
c) Poisson Distribution
d) Binomial Distribution
Answer: a
Clarification: f (x) = λ^α x^α−1 e^−λx / Γ(α) for x > 0
= 0 otherwise
If we let α=1, we obtain
f(x) = λe^−λx for x > 0
= 0 otherwise.
Hence we obtain Exponential Distribution.

3. Sum of n independent Exponential random variables (λ) results in __________
a) Uniform random variable
b) Binomial random variable
c) Gamma random variable
d) Normal random variable
Answer: c
Clarification: Gamma (1,λ) = Exponential (λ).
Hence Exponential (λ₁) + Exponential (λ₂) + Exponential (λ₃)….. n times = Gamma(n,λ).

4. Find the value of Γ(5/2).
a) 5/4 . π^1/2
b) 7/4 . π^1/2
c) 1/4 . π^1/2
d) 3/4 . π^1/2
Answer: d
Clarification: By the property of Gamma Function
Γ(α+1) = αΓ(α)
(Γ(frac{5}{2}) = frac{3}{2} ⋅ Γ(frac{3}{2}) )
(= frac{3}{2} ⋅ frac{1}{2} . Γ(frac{1}{2}) )
(= frac{3}{2} ⋅ frac{1}{2} ⋅ π^{1/2} ) By property of Gamma function (Γ(frac{1}{2}) = π^{1/2} )
(= frac{3}{4} . π^{1/2}. )

5. Gamma function is defined as Γ(α) = ₀∫^∞ x^α−1 e^−x dx.
a) True
b) False
Answer: a
Clarification: The Gamma function is defined as Γ(α) = ₀∫^∞ x^α−1 e^−x dx. Gamma function can also be defined as Γ(α+1) = αΓ(α).

6. Gamma distribution is Multi-variate distribution.
a) True
b) False
Answer: b
Clarification: Gamma distribution is a uni-variate distribution that means it is only defined for x ranging from (0, ∞).

7. Which of the following graph represents gamma distribution?
a)
b)
c)
d)
Answer: a
Clarification: Gamma distribution is defined as
f(x) = λ^α x^α−1 e^−λx / Γ(α) for x > 0.
Hence it is an exponentially decreasing function.