If X is a random variable with distribution given below Then the value of k and its variance are respectively given by

Step-by-step solution

The sum of all the probabilities in a probability distribution is always unity. array ll & k+3 k+3 k+k=1 & 8 k=1 & k= 1 8 array aligned E ( X ) & = x_ i P (x_ i ) & =0 ( 1 8 )+1 ( 3 8 )+2 ( 3 8 )+3 ( 1 8 )= 3 2 aligned Var (X)=E (X^2 )-[E(X)]^2 aligned & =0^2 ( 1 8 )+1^2 ( 3 8 )+2^2 ( 3 8 )+3^2 ( 1 8 )- ( 3 2 )^2 & = 3 4 aligned