Skip to content
We use only essential cookies to keep you signed in and remember your preferences. See our Cookie Policy.
TestStop
MocksPracticeResourcesIndiaBlogPricing
Sign in
Questions › DSE › DSE 2008 › Q29
2 marksStatistics › Joint distributions, covariance and correlation › Joint, marginal and conditional distributionsHardabout 4 min

DSE 2008 Question 29: Joint distributions, covariance and correlation

Each cell of the following table gives the joint probability of (X,Y)(X,Y)(X,Y). For X=1X=1X=1: Y=1→.1Y=1\to.1Y=1→.1, Y=2→0Y=2\to0Y=2→0, Y=3→.1Y=3\to.1Y=3→.1, Y=4→0Y=4\to0Y=4→0. For X=2X=2X=2: .3,0,.1,.2.3, 0, .1, .2.3,0,.1,.2. For X=3X=3X=3: 0,.1,0,.10, .1, 0, .10,.1,0,.1. Consider: I. Pr⁡(Y=2)>Pr⁡(X=1)\Pr(Y=2)>\Pr(X=1)Pr(Y=2)>Pr(X=1); II. Pr⁡(Y=1∣X=2)=Pr⁡(Y=1∣X=1)\Pr(Y=1\mid X=2)=\Pr(Y=1\mid X=1)Pr(Y=1∣X=2)=Pr(Y=1∣X=1); III. The events X=3X=3X=3 and Y=3Y=3Y=3 are mutually exclusive; IV. X and Y are independent. Which are true?

Tap an option to check your answer.

Answer and worked solution

Checking your account…

Plain-text version

Each cell of the following table gives the joint probability of (X,Y). For X=1: Y=1→.1, Y=2→0, Y=3→.1, Y=4→0. For X=2: .3, 0,.1,.2. For X=3: 0,.1, 0,.1. Consider: I. Pr (Y=2)>Pr (X=1); II. Pr (Y=1| X=2)=Pr (Y=1| X=1); III. The events X=3 and Y=3 are mutually exclusive; IV. X and Y are independent. Which are true? (A) only I and II. (B) only II and III. (C) only III and IV. (D) only II, III and IV.

Also written as: Each cell of the following table gives the joint probability of (X,Y). For X=1: Y=1->.1, Y=2->0, Y=3->.1, Y=4->0. For X=2: .3, 0,.1,.2. For X=3: 0,.1, 0,.1. Consider: I. Pr (Y=2)>Pr (X=1); II. Pr (Y=1| X=2)=Pr (Y=1| X=1); III. The events X=3 and Y=3 are mutually exclusive; IV. X and Y are independent. Which are true?

Joint distributions, covariance and correlation has come up 61 times in 7 exams since 2005.

What this question tests

This question is on Joint, marginal and conditional distributions, part of Joint distributions, covariance and correlation in Statistics.

How two random variables behave together and separately.

TestStop has 14 past-paper questions on this subtopic.

Practise Joint distributions, covariance and correlationMore on Joint, marginal and conditional distributions

Similar questions from other papers

  • CUET-PG 2025 · Q22In correlation analysis, the two variables
  • IIT JAM 2025 · Q41The correlation coefficient between x and y using the following information is (*rounded off to two decimal places*). Σᵢ₌₁¹⁰⁰ xᵢ=280, Σᵢ₌₁¹⁰⁰ yᵢ=60, Σᵢ₌₁¹⁰⁰ xᵢ²=2384,
  • UGC-NET 2025 · Q83Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): If X and Y are any two variables transformed to…
  • GATE 2024 · Q48If X and Y are two random variables with the joint probability density function f(x,y) = { 2/3(x+2y) for 0<x,y<1; 0 otherwise } then E[X | Y=1/2] will be
  • IIT JAM 2024 · Q35Let X have mean μₓ, variance σₓ², and Y mean μ_y, variance σ_y², with correlation ρ. Which of the following is/are CORRECT?

Question from the DSE 2008 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.