Suppose that X is a finite random variable such that E(X) = 12.30 and E(X^2) = 1

Question

Suppose that X is a finite random variable such that E(X) = 12.30 and E(X^2) = 152.10 Find the standard deviation oX of X. Suppose that X is a finite random variable such that E(X) = 12.30 and E(X^2) = 152.10. Put Y = 7X - 85. E(Y). Suppose that X is a finite random variable such that E(X) = 12.30 and E(X^2) = 152.10. Put Y = 7X - 85. Find the standard deviation oY of Y. Suppose that X is a finite random variable such that E(X) = 12.30 and E(X^2) = 152.10. Create a new random variable Z be repeating X sixteen times, and adding the values. Find E(Z). Suppose that X is a finite random variable such that E(X) = 12.30 and E(X^2) = 152.10. Create a new random variable Z be repeating X sixteen times, and adding the values. Find the standard deviation of Z.

Explanation / Answer

Given that X is a finite random variable such that

E(X) = 12.30 and E(X2) = 152.10

Z = 16X

E(Z) = (16X)

= 16  E(X)

= 16*12.30

= 196.8

E(Z2) = E[(16X)2 ] = 256*E(X2) = 256*125.10 = 38937.6

Var(Z) = 38937.6 - 196.82 = 207.36

Sd(Z) = sqrt(207.36) = 14.4

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