Math Problem Statement
The joint probability distribution table for two random variables X and Y is as follows Y X -2 -1 4 5 1 0.1 0.2 0 0.3 0.1 0.1 0 2 0.2 Determine the marginal probability distributions of X and Y. Also compute (a) Expectations of X and Y (b) Standard deviation of X and Y (c) Covariance of X and Y (d) Correlation of X and Y.
Solution
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Math Problem Analysis
Mathematical Concepts
Probability Theory
Marginal Distributions
Expectation
Variance
Covariance
Correlation
Formulas
Marginal distribution of X: P(X = x) = Σ P(X = x, Y = y)
Expectation of X: E(X) = Σ x * P(X = x)
Variance of X: Var(X) = E(X^2) - [E(X)]^2
Covariance: Cov(X, Y) = E(XY) - E(X)E(Y)
Correlation: Corr(X, Y) = Cov(X, Y) / (σ_X * σ_Y)
Theorems
Law of Total Probability
Covariance and Correlation Definitions
Suitable Grade Level
Undergraduate Level (Probability and Statistics)
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