Joint Distributions

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Each question is graded on a single answer: a check that this chapter's methods work, not a test of the reasoning behind them.

For the joint pmf

p (x, y)

of ⁠

(X, Y)

on ⁠

{0, 1, 2}^{2}

given by the table with rows

x = 0, 1, 2

and columns

y = 0, 1, 2

⁠:

x = 0 x = 1 x = 2 y = 0 1/12 2/12 1/12 y = 1 1/12 1/12 2/12 y = 2 2/12 1/12 1/12

Compute

p (1, 2)

⁠.

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About these 107 questions

Two or more random variables on one probability space: joint pmfs and densities, marginals, independence, conditional distributions, the bivariate normal, and sums by convolution. This set covers the chapter Joint Distributions in Probability: 33 easy, 47 medium and 27 hard questions, each graded instantly with a hint and a full step-by-step solution. Progress is saved in this browser only.

Joint mass functions, densities and the joint cdf — 15 questions
Marginal distributions — 14 questions
Independence of random variables — 14 questions
Conditional distributions — 14 questions
Several variables: pairwise and mutual independence — 10 questions
Functions of two variables and two-dimensional LOTUS — 13 questions
The bivariate normal distribution — 13 questions
Sums of independent random variables: convolution — 14 questions