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4 X is a random variable with E(X) = 100 and V(X) = 15. Find (a) E(X2). (b) E(3X + 10). (c) E(-X). (d) V(-X). (e) D(-X).

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Answer #1

Answer:

Given,

Mean = E(X) = 100

Variance = V(X) = 15

a)

E(X^2) = V(X) + [E(X)]^2

substitute values

= 15 + 100^2

= 10015

b)

E(3X+10) = 3*E(X) + 10

= 3*100 + 10

= 310

c)

E(-X) = - E(X)

= - 100

d)

V(-X) = (-1)^2*V(X)

= (-1)^2 *15

= 15

e)

D(-X) = sqrt(V(-X))

= sqrt(15)

= 3.873

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