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15. Probobility, Ex. (1)., , Distribution, , A rqndom voriqble X hqs the following probobility distribution, , :, , P(X, , :, , x), , Find(i)k(ii)p(x<3)(iii)p(x>2)(iv)P(0<x<a)(v)P(2<x<5), Solution : For o rqndom vorioble Xwehove, , :. k+3k+ 5k+7k+9k+, , (i) k:, , :, , o,=', , i=l, , llk+l3k:l, , k:L49, , i.e.49k:13, P(X, , f, , x), , qs, , (iD P(X < 3) : P(X, , : 0) + P(x :1) + P(X:2), , -49 49 49 49, (iii)P(x22):P(X:2)+P(X:3)+P(X:4)+P(X:5)+P(X:6), (iv)P(0 < X < 4) : P(X: 1) + P(X : 2) + P(X : 3), (v) P(2 < X <5), , Ex., , (2)., , :, , P(X, , :, , 2) +P(X, , :, , 3) + P(X, , :, , 4) + P(X, , :, , 5), , s 7 9 ll 32, :49+, *+ 49* qg:49, , Colculqte the Expected volue ond vorionce of x if x denotes the, number obtoined on the uppermost fqce when o fqir die is thrown., , :, Solution : When o foir die is thrown, the somple spoce is ^S {1,2, 3, 4, 5, 6\ ', Let X denotes the number obtoined on the uppeflnost foce., .'. Xcqn toke volues l, 2, 3, 4, 5', 6', :, : :, : :, P(X : l) : P(X : 2) : P(X : 3) : P(X 4) P(X 5) P(X 6), I, 6, , The probobilitY distribution is, , ffim', Aurangabad), Satish Jadhwar ( Sant Meera Jr' College', , '