4. Suppose that X is a random variable having the following probability distri- bution function -...

Question

Question

Answer 1

Answer #1

a)

below is probability mass function of X:

P(X=1)=P(X<=1)-P(X<1)=1/2-0 =1/2

P(X=3)=P(X<=3)-P(X<3)=2/3-1/2=1/6

P(X=6)=P(X<=6)-P(X<6)=1-2=1/3

b)

from above expectation =3

and Variance =5

c)

P(4<=X<6)=0 (as no value exist between 4 and 6 for which X has any probabilistic value)

P(1<X<6)=P(X=3)=1/6

d)

E(3X-6X²)=3E(X)-6E(X²)=3*3-6*14=-75

Var(3X-4)=9*Var(X)=9*5=45

Answer 2

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