2. Prove the following properties of expectation and variance: If a and b are constants, X and Y are random variables, then E(aX+b)=aE(x)+b var (aX+ b) = a? var (X) var (X+ Y)= var (X) + var (Y) + 2 cov(X, Y) =var (X) + var (Y) + 2po;0y Of which p is correlation coefficient, Ox and oy are standard error of X and Y. 3. Assume that X N(6, 4). What is the probability that 2 10?

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2. Prove the following properties of expectation and variance:
If a and b are constants, X and Y are random variables, then
E(aX+b)=aE(x)+b
var (aX+ b) = a? var (X)
var (X+ Y)= var (X) + var (Y) + 2 cov(X, Y)
=var (X) + var (Y) + 2po;0y
Of which p is correlation coefficient, oz and o, are standard error of X
and Y.
3. Assume that X- N(6, 4). What is the probability that 2 <X<10, and
what is the probability that X>10?
Transcribed Image Text:2. Prove the following properties of expectation and variance: If a and b are constants, X and Y are random variables, then E(aX+b)=aE(x)+b var (aX+ b) = a? var (X) var (X+ Y)= var (X) + var (Y) + 2 cov(X, Y) =var (X) + var (Y) + 2po;0y Of which p is correlation coefficient, oz and o, are standard error of X and Y. 3. Assume that X- N(6, 4). What is the probability that 2 <X<10, and what is the probability that X>10?
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