ISS 2025 Statistics Paper 1 Solution Questions 16 to 20

ISS 2025 Statistics Paper 1 Questions 16 to 20 complete solution with detailed explanation. Question 16 covers joint probability mass function, Question 17 explains geometric distribution, Question 18 discusses bivariate normal distribution, Question 19 is based on correlation coefficient and hypothesis testing, while Question 20 focuses on association between attributes.

Q. 16 The following is the joint probability mass function of two random variables X and Y :

Y \ X	0	1	2
0	3/28	9/28	3/28
1	3/14	3/14	0
2	1/28	0	0

Which of the following statements is/are correct ?

I. Cov(X, Y) = 3/4

II. E(X) = E(Y)

Select the answer using the code given below :

(a) I only

(b) II only

(c) Both I and II

(d) Neither I nor II Q. 17 Let (X₁, X₂, . . . , Xₖ) be a random sample of size k from geometric distribution with parameter p with pmf f(x) = pq^(x−1), x = 1, 2, 3, . . . . Then min(X₁, X₂, . . . , Xₖ) is distributed geometrically with parameter :

(a) 1 − pᵏ

(b) 1 − (1 − p)ᵏ

(c) (1 − p)ᵏ

(d) None of the above Q. 18 If the random variables X and Y have a bivariate normal distribution with parameters μ₁, μ₂, σ₁², σ₂² and ρ, then the marginal distribution of X is :

(a) N(μ₁, σ₁²)

(b) N(μ₁ + ρ · σ₁/σ₂ · (y − μ₂), σ₁²)

(c) N(μ₁, σ₁²(1 − ρ²))

(d) N(μ₁ + ρ · σ₁/σ₂ · (y − μ₂), σ₁²(1 − ρ²))

Q. 19 What would be the lowest value of r² in a sample of 27 pairs of observations which would be significant at 5% level of significance ? [t₂₅(0.05) = 2.06]

(a) 0.1451

(b) 0.2451

(c) 0.3551

(d) 0.4451 Q. 20 The male population in a state is 25 lakh. Among them the number of literates is 2 lakh, the number of criminals is 26000 and the number of literate criminals is 2000. What is the association between literacy and criminality ?

(a) No association

(b) Negatively associated

(c) Positively associated

(d) Association cannot be established

Answer in Bilingual