A player tosses 2 fair coins. He wins ₹ 5 if 2 heads appear, ₹ 2 if one head appears and ₹ 1 if no head appears. Then the variance of his winning amount in ₹ is

Step-by-step solution

When player tosses 2 fair coins, then S = HH , HT , TH , TT Let X be a random variable that denotes the amount received by player. Then, X can take values 5,2 and 1 Now, P ( X =5)= 1 4 , P ( X =2)= 1 2 and P ( X =1)= 1 4 The probability distribution of X is as follows: array |c|c|c|c| X & 5 & 2 & 1 P ( X ) & 1 4 & 1 2 & 1 4 array aligned Variance of X & = X ^2 P ( X )-[ XP ( X )]^2 & = [ 25 4 +2+ 1 4 ]- [ 5 4 +1+ 1 4 ]^2 & = 34 4 - ( 10 4 )^2 & = 34 4 - 25 4 & = 9 4 aligned