Pui Yan L.

asked • 11/16/22

The probability function fX for a random variable X is given by the table below.

The probability function fX for a random variable X is given by the table below.

x | -1 0 1 2 3

fX(x) = P(X = x)| 0.2 0 u 0.2 0.1

(a) Find u.

(b) Find the expected value and variance of the distribution for the random variable X: E(X) and Var(X).

(c) Assume now Y = X − 2, then you may regard Y as another random variable. Find the expected value and variance for the distribution of this random variable Y : E(Y ) and Var(Y ).

(d) No need to answer this part. Just a remark for your interest: In part (c), you are finding E(X − 2) and Var(X − 2). It would be interesting to compare these values with E(X) and Var(X), and observe that E(Y ) = E(X) − 2 and Var(Y ) = Var(X).


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