ISS 2025 Statistics Paper 1 Solution Questions 1 to 5
- Gajender Raaz
- 5 hours ago
- 2 min read
ISS 2025 Statistics Paper 1 MCQs and Solutions Questions 1-5
In this blog, we discuss ISS 2025 Statistics Paper 1 Questions 6-10 with complete solutions and detailed explanations. These questions cover important topics such as Laplace Distribution, Joint Probability Density Function, Expectation, Moment Generating Function (MGF), and Chi-Square Distribution.
These MCQs are highly useful for ISS aspirants, UGC NET Statistics students, MSc Statistics students, and all competitive exam preparations related to Probability and Mathematical Statistics.
Q. 6 The distribution function of standard Laplace distribution with the pdf
f(x) = 1/2 · e^(−|x|), −∞ < x < ∞ is :
(a) F_X(x) = eˣ/2, x ≤ 0 F_X(x) = 1 − e^(−x)/2, x > 0
(b) F_X(x) = eˣ/2, x ≤ 0 F_X(x) = (1 − e^(−x))/2, x > 0
(c) F_X(x) = e^(−x)/2, x ≤ 0 F_X(x) = eˣ/2, x > 0
(d) F_X(x) = (1 − e^(−x))/2, x ≤ 0 F_X(x) = 1, x > 0
Q. 7 Let X₁ and X₂ have the joint pdf given by
f(x₁, x₂) = 2, 0 < x₁ < x₂ < 1 f(x₁, x₂) = 0, otherwise
What is the marginal distribution of X₁ ?
(a) f₁(x₁) = 1, 0 < x₁ < 1
(b) f₁(x₁) = 2 − 2x₁, 0 < x₁ < 1
(c) f₁(x₁) = 2x₁, 0 < x₁ < 1
(d) f₁(x₁) = 3x₁², 0 < x₁ < 1
Q. 8 Let k > 0 be a constant such that pdf of X is given by
f(x) = kx(1 − x), 0 < x < 1 f(x) = 0, elsewhere
What is the value of E(X) ?
(a) 1/2
(b) 1/4
(c) 1/6
(d) 1/8
Q. 9 Let M_X(t) and M_Y(t) be the moment generating functions of two random variables X and Y respectively, for some t ∈ R. If E(X) = 1/2, Var(X) = 1/4 and M_Y(t) = (0.75 + 0.25e^(2t))M_X(t), where t ∈ (−h, h); h > 0, then what is Var(Y) equal to ?
(a) 1/4
(b) 1/2
(c) 1
(d) 2
Q. 10 Let X follow Chi-square distribution with n degrees of freedom. Which of the following statements is/are correct ?
I. (X − n) / √(2n) is asymptotically normally distributed with mean 0 and variance 1.
II. X/n is asymptotically normal with mean 1 and variance 2/n.
Select the answer using the code given below :
(a) I only
(b) II only
(c) Both I and II
(d) Neither I nor II
Answer in English
Answer in Bilingual
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