If a discrete random variable X has probability distribution as follows array |c|c|c|c|c| X =x & 0 & 1 & 2 & 3 P [ X =x] & k & 3 k & 3 k & k array Then var ( X )=

Step-by-step solution

Here k +3 k +3 k + k =8 k =1 k = 1 8 aligned P _ ( x ₁ ) x _ i &=0 1 8 +1 3 8 +2 3 8 +3 1 8 = 12 8 = 3 2 and P _ ( x _ i ) x _ i ² &= (0 1 8 )+ (1 3 8 )+ (4 3 8 )+ (9 1 8 )= 24 8 =3 Variance &= V ( X ) &= P _ ( x _ i ) x _ i ²- [ P _ ( x _ i ) x _ i ]² &=3- ( 3 2 )²=3- 9 4 = 3 4 aligned