Three fair coins with faces numbered 1 and 0 are tossed simultaneously. Then variance ( X ) of the probability distribution of random variable X , where X is the sum of numbers on the upper most faces, is

Step-by-step solution

Possible value of X are 0,1,2,3 Here, S = 000,001,010,1,00,111,110,101,011 n ( S )=8 aligned & E ( X )= x_ i p _ i =0+ 3 8 + 6 8 + 3 8 = 12 8 & E ( X ^2 )= & x_ i ^2 p _ i ^2=0+ 3 8 + 12 8 + 9 8 = 24 8 & =3- ( 3 2 )^2 & =3- 9 4 & = 3 4 & =0.75 aligned