Let X be a random variable with support 2 1 a where a is a r

Let X be a random variable with support {?2, 1, a}, where a is a real number, P(X = ?2) = 1/2, P(X = 1) = 1/3,

and E(X) = 0.

Find the value of a.

sum of probability of random variable is one.

P(x=a)+P(x=-2)+P(x=1)=1

P(x=a) = 1 - ( P(x=-2)+P(x=1) )

=1 - (0.5+1/3)

P(x=a) = 0.167

E(x) = a*P(x=a) - 2*P(x=-2) + 1*P(x=1)

=>a*0.167 - 2*0.5 + 1/3 = 0

a = (2*0.5 - 1/3)/0.167

= 3.999

=4.