Question

A player tosses 2 fair coins. He wins Rs. 5 If 2 heads appear, Rs. 2 If 1 head appear and Rs.1 if no head appears, then variance of his winning amount is ______.

Options

• 6

• `5/2`

• `9/4`

• `17/2`

Answer 1

A player tosses 2 fair coins. He wins Rs. 5 If 2 heads appear, Rs. 2 If 1 head appear and Rs.1 if no head appears, then variance of his winning amount is `underline(9/4)`.

Explanation:

When player tosses 2 fair coins then

S = {HT, TH, TT, HH}

Let X be a random variable that denotes the amount received by the player.

Then, X can take value 5, 2 and 1.

Now, P(X = 5) = `1/4`, P(X = 2) = `2/4 = 1/2` and P(X = 1) = `1/4`

Thus, the probability distribution of X is

X	5	2	1
P(X)	`1/4`	`1/2`	`1/4`

∴ Variance of X = `sum "X"^2 "P"("X") - [sum "X" "P"("X")]^2`

Now, `sum "X P"("X") = 5 xx 1/4 + 2 xx 1/2 + 1 xx  1/4`

`= 5/4 + 4/4 + 1/4 = 10/4 = 5/2`

∴ Variance of X = `sum "X"^2 "P"("X") - [sum "X" "P"("X")]^2`

`= (25 xx 1/4 + 4 xx 1/2 + 1 xx 1/4) - (5/2)^2`

`= ((25 + 8 + 1)/4) - 25/4 = 9/4`