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

Step-by-step solution

Three fair coins numbered 1,0 are tossed. Sample space = 111,110,101,011,100,010 , 001,000 n ( S )=8 X represents the sum of numbers on upper most face aligned & P(X=0)= 1 8 , & P(X=1)= 3 8 , & P(X=2)= 3 8 , & P(X=3)= 1 8 aligned Probability distribution of X is array |c|c|c|c|c| X & 0 & 1 & 2 & 3 P ( X ) & 1 8 & 3 8 & 3 8 & 1 8 array aligned E ( X ) & = _ x=0 ^3 x_ i P (x_ i ) E ( X ) & =0 1 8 +1 3 8 +2 3 8 +3 1 8 & = 12 8 = 3 2 E ( X ^2 ) & = _ x=0 ^3 x₁^2 P (x_ i )=3 Variance of X & = E ( X ^2 )-[ E ( X )]^2 & =