7 If a discrete random variable X has the following probabil

7. If a discrete random variable X has the following probability distribution:

X      -2 - 1 0 1 2

P(X) 0.2 0.3 0.15 0.2 0.15

Use this to find the following:

(a) The mean of X and E[X^2].

(b) The probability distribution for Y = 2X^2 + 2 (i.e, all values of Y and P(Y )).

(c) Using part (b) (i.e, the probability distribution forY ), find E[Y ].

(d) Using part (a), verify your answer in part (c) for E[Y ].

Solution

E(X) =-0.2

E(X²) =1.9

(b) The probability distribution for Y = 2X^2 + 2

E(Y) = 5.8 using pdf

E(Y) =E(2x^2+2) = 2E(X^2)+2 = 3.8+2

=5.8

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