A random variable X takes values 0,1,2,3 with probabilities 2 a+1 30 , 8 a-1 30 , 4 a+1 30 , b respectively, where a , b R . Let and respectively be the mean and standard deviation of X such that ²+ ²=2 . Then a b is equal to :

Step-by-step solution

Sum of probabilities = 1 : 2a+1+8a-1+4a+1 30 + b = 1 b = 29-14a 30 . ^2 + ^2 = E(X^2) = 2 . E(X^2) = 8a-1 30 + 4(4a+1) 30 + 9(29-14a) 30 = -102a + 264 30 = 2 . -102a + 264 = 60 a = 2 . b = 29 - 28 30 = 1 30 . a b = 2 1/30 = 60 .