Question

In: Statistics and Probability

Let X be a random variable with mean ux=20 and standard deviation x = 3 and...

Let X be a random variable with mean ux=20 and standard deviation x = 3 and let Y be a random variable with mean uy=28 and standard deviation y =3. It is known that X and Y are independent random variable. A new random variable U is created where U=Y-X. what is the standard deviation of U?

Expert Solution

X and Y are independent random variable

standard deviation of X = 3

Var(X) = variance of X = 9

standard deviation of Y = 3

Var(Y) = variance of Y = 9

U = Y-X

Var(U) = Var(Y-X)

Var(U) = Var(Y) +Var(X) - 2Cov(X,Y)

[ Cov(X,Y) is covariance of X and Y

Here Cov(X,Y)=0 as X and Y are indepenent]

So, Var(U) = Var(Y) +Var(X)

Var(U) = 9 + 9 = 18

standard deviation of U = = 4.2426

Answer : Standard deviation of U is or 4.2426

orchestra answered 2 years ago

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