The probability distribution for a random variable X is give

The probability distribution for a random variable X is given by Pr(X = x) = (3x + 1)/22

x = 0; 1; 2; 3. Determine

(A) Pr(X = 3)

(B) Pr(X <=1)

(C) Pr(X > -2)

(D) Pr(1 <= X < 3)

Solution

Pr(X = x) = (3x + 1)/22

CDF,C(x) = P(X<=x) = integration Pr(X=x)
C(x) = (1/22) * ((3/2)*(x^2) + x)

(A) Pr(X = 3)
= (3*3 + 1)/22
= 5/11
= 0.4545

(B) Pr(X <=1)
= C(1)
= (1/22) * ((3/2)*(1^2) + 1)
= 0.1136

(C) Pr(X > -2)
= 1 - Pr(X<= -2)
= 1 - C(-2)
= 1 - ((1/22) * ((3/2)*(4) - 2))
= 0.8182

(D) Pr(1 <= X < 3)
= C(3) - C(1)
= ((1/22) * ((3/2)*(9) + 3)) - ((1/22) * ((3/2)*(1) + 1))
= 0.6364