Question

Suppose that X and Y are random variables with E(X) = 2, E(Y) = 1, E(X²) = 5, E(Y²) = 10, E(XY) = 1. Problem 10: Find Cor(X, Y) and Var(X + Y). {HINT: The correlation of a bivariate (X, Y) is given by cor(X, Y) = \frac{Cov(X,Y)}{\sqrt{Var(X)Var(Y)}} Problem 11: Assume that X + Y is normally distributed. Find P(X + Y < 5)

          Suppose that X and Y are random variables with
E(X) = 2, E(Y) = 1, E(X²) = 5, E(Y²) = 10, E(XY) = 1.
Problem 10: Find Cor(X, Y) and Var(X + Y).
{HINT: The correlation of a bivariate (X, Y) is given by cor(X, Y) = \frac{Cov(X,Y)}{\sqrt{Var(X)Var(Y)}}
Problem 11: Assume that X + Y is normally distributed. Find P(X + Y < 5)

Suppose that X and Y are random variables with
E(X) = 2, E(Y) = 1, E(X²) = 5, E(Y²) = 10, E(XY) = 1.
Problem 10: Find Cor(X, Y) and Var(X + Y).
HINT: The correlation of a bivariate (X, Y) is given by cor(X, Y) = (Cov(X,Y))/(√(Var(X)Var(Y)))
Problem 11: Assume that X + Y is normally distributed. Find P(X + Y < 5)

Added by Lisa B.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Suppose that X and Y are random variables with E(X) = 2, E(Y) = 1, E(X^2) = 5, E(Y^2) = 10, E(XY) = 1. Problem 10: Find Cov(X, Y) and Var(X + Y). Cov(X, Y) {HINT: The covariance of a bivariate (X, Y) is given by Cov(X, Y) = E(XY) - E(X)E(Y)} [5] Problem 11: Assume that X + Y is normally distributed. Find P(X + Y < 5) [5]