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A given a random variable x with mean 10 and variance 9


a) Given a random variable x with mean 10 and variance 9, find the expected value and variance of the random variable y where y = 12 + 2x.

b) A random variable x has E[x]=5 and Var(x)=9. A random variable y, independent of x, has E[y]=10 and Var(y)=25.

  1. Find E[xy], E[x+2y], E[13-2x]
  2. Find Var(x-y), Var(x+2y), Var(13-2x)
  3. Cov(x,y)

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Basic Statistics: A given a random variable x with mean 10 and variance 9
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