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)
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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) (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  = 5)
, we have  + 9p = 5)
or 
. So p = 1/2, so
P(X = 1) = 1/2
P(X = 2) = 0
P(X = 3) = 1/2
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