Expected Value, Variance and Covariance of random variable
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1. Say that E(X) = 10; and var(X) = 5. Find E(Y) and var(Y) in the following cases:
a) Y = 0.37X - 3.79
b) Y = 0.37X + 5.73
c) Y = (3x^2+2)/4
d) Y = aX + b
2. Prove that:
a) E(X^2) greater than equal to [E(X)]^2 (Hint: this follows immediately from the definition of the variance and from one of the properties of the variance).
b) cov(X, Y ) = E(XY )- , where = E(X) and = E(Y ). (Hint: Use the definition
of covariance).
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Solution Summary
Calculation of Expected Value E(X), Variance V(x) and Covariance of random variable.
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1. Say that E(X) = 10; and var(X) = 5. Find E(Y) and var(Y) in the following cases:
a) Y = 0.37X - 3.79
b) Y = 0.37X + 5.73
c) Y = (3x^2+2)/4
d) Y = aX + b
Answer
We have the result
E(aX+b) = aE(X)+b
V(aX+b) =a2V(X)
a). ...
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