Question

If three fair coins are tossed, where X = number of tails obtained, then Var(X) is ______ 

विकल्प

• `1/2`

• `3/2`

• `2/3`

• `3/4`

Answer 1

If three fair coins are tossed, where X = number of tails obtained, then Var(X) is `underline(3/4)`.

Explanation:

X can take values 0, 1, 2 and 3.

P(X = 0) = Probability of getting no tail = `1/8`

P(X = 1) = Probability of getting one tail = `3/8`

P(X = 2) = Probability of getting two tails = `3/8`

P(X = 3) = Probability of getting three tails = `1/8` 

∴ E(X) = `sumx_i . P(x_i)`

`= (0)(1/8) + (1)(3/8) + (2)(3/8) + (3)(1/8)`

= `3/2`

`E(X^2) = sumx_1^2 . P(x_i)`

= `(0)^2(1/8) + (1)^2(3/8) + (2)^2(3/8) + (3)^2(1/8)`

= 3

Var(X) = E(X²) - [E(X)]²

`= 3 - (3/2)^2`

= `3/4`