SOLUTION: A random variable x has the possible values 1, 2, and 3. E(X)=2 and E(X^2)=5. Find P(X=1), P(X=2), and P(X=3)

Algebra ->  Probability-and-statistics -> SOLUTION: A random variable x has the possible values 1, 2, and 3. E(X)=2 and E(X^2)=5. Find P(X=1), P(X=2), and P(X=3)      Log On


   

Question 1029572: A random variable x has the possible values 1, 2, and 3. E(X)=2 and E(X^2)=5. Find P(X=1), P(X=2), and P(X=3)
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Since E(X) = 2, we must have P(X = 1) = P(X = 3) = p and P(X = 2) = 1-2p for some p.

Since , we have or . So p = 1/2, so

P(X = 1) = 1/2
P(X = 2) = 0
P(X = 3) = 1/2