ISS 2025 Statistics Paper 1 Solution Questions 11 to 15

ISS 2025 Statistics Paper 1 Questions 11 to 15 complete solution with detailed explanation. Question 11 covers Probability concepts, Question 12 explains Distribution Theory, Question 13 discusses Statistical Inference, Question 14 focuses on Random Variables, and Question 15 is based on Mathematical Statistics concepts useful for ISS exam preparation.

ISS 2025 Statistics Paper 1 Solution Questions 11 to 15

Q. 11 The joint probability of the occurrence of two events A and B is given by the following contingency table:

B B̅

A 0.4 0.1

A̅ 0.2 0.3

Consider the following statements:

I. A and B are independent events.

II. P(A | B̅) + P(A̅ | B) = 1/2

Which of the statements given above is/are correct?

(a) I only

(b) II only

(c) Both I and II

(d) Neither I nor II

Q. 12 If kᵣ and μ′ᵣ denote respectively the rᵗʰ cumulant and the rᵗʰ moment about origin zero of a distribution, then which of the following statements are correct?

I. k₁ = μ′₁

II. k₂ = μ′₂ − μ′₁²

III. k₃ = μ′₃ − 3μ′₂μ′₁ + 2μ′₁³

Select the answer using the code given below:

(a) I and II only

(b) II and III only

(c) I and III only

(d) I, II and III

Q. 13 Let (X, Y) follow bivariate normal distribution with E(X) = E(Y) = 2, V(X) = 100, V(Y) = 144 and Corr(X, Y) = 0.5. Which of the following statements is/are correct?

I. E(Y | X = x) = 3.2 + 0.6x

II. V(Y | X = x) = 108

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. 14 In a trivariate distribution, it is given that

r₁₂ = 0.8, r₁₃ = −0.4, r₂₃ = 0.

The value of correlation coefficient between X₁ and X₃ after linear effect of X₂ on each of them is eliminated, is:

(a) 2/3

(b) 1/3

(c) −1/3

(d) −2/3

Q. 15 If ηYX is the correlation ratio of Y on X, then which of the following statements is/are correct?

I. η²YX is independent of change of origin and scale.

II. ηYX = ηXY

III. η²YX ≥ r² where r is the correlation coefficient between X and Y.

Select the answer using the code given below:

(a) I and II only

(b) III only

(c) I and III only

(d) I, II and III

Answer in Bilingual

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Answer in English