Two numbers are selected are random (withoutreplacement) from positive integers 2, 3, 4, 5, 6 and 7. Let X denote the largerof the two numbers obtained. Find the mean and variance of the probability distribution of X.

Two numbers are selected are random (withoutreplacement) from positive

1.	Two numbers are selected are random (withoutreplacement) from positive integers 2, 3, 4, 5, 6 and 7. Let X denote the largerof the two numbers obtained. Find the mean and variance of the probability distribution of X.
Answer» Here are some positive integers `(2,3,4,5,6,7)` from which two numbers are selected at random (without replacement) and from those selected numbers larger one is selected. Smallest pair that can be formed `(2,3)` and Largest pair `(6,7)` therefore minimum value for X is `3` and maximum is `7`. `P(X=3) = P{(2,3),(3,2)} = P(2,3) + P(3,2)``=1/61/5+1/61/5` `P(X=3) = 1/15`Similarly, `P(X=4) = 2/15` `P(X=5) = 1/5` `P(X=6) = 4/15` `P(X=7) = 1/3` `Mean = Sigmax . P(X=x)= 3(1)/15+4(2)/15+5(3)/15+6(4)/15+7(5)/15` `=1/15[3+8+15+24+35]` `=85/15=5.67` `E(x^2)=3^21/15+4^22/15+5^23/15+144/15+245/15` `=1/15[9+32+75+144+245]``=33.67`Therefore, Variance `(x)= E(E^2)-E(X)^2` `=33.67-(5.67)^2``=1.52`