Re: Maths JNU

Posted by Amit Goyal on Apr 05, 2010; 12:35pm
URL: http://discussion-forum.276.s1.nabble.com/Maths-JNU-tp4850609p4853294.html

Hi Chandrani,
Since dice is independently rolled three times, probability distribution of Xi is:
P(Xi = 0) = P(Even number on ith roll) = 2/3
P(Xi = 1) = P(Odd number on ith roll) = 1/3

Probability distribution of Y is
P(Y = 0) = P(X1 = X2 = X3 = 0) = 8/27
P(Y = 1) = P(X1 = X2 = 0, X3 = 1) + P(X1 = X3 = 0, X2 = 1) + P(X2 = X3 = 0, X1 = 1) = 12/27
P(Y = 2) = P(X1 = X2 = 1, X3 = 0) + P(X1 = X3 = 1, X2 = 0) + P(X2 = X3 = 1, X1 = 0) = 6/27
P(Y = 3) = P(X1 = X2 = X3 = 1) = 1/27

Mean(Y) = 1 Variance(Y) = 2/3