Question

Kiran plays a game of throwing a fair die 3 times but to quit as and when she gets a six. Kiran gets +1 point for a six and –1 for any other number.

1. If X denotes the random variable “points earned” then what are the possible values X can take?
2. Find the probability distribution of this random variable X.
3. Find the expected value of the points she gets.

Answer 1

i. X = −3, −1, 0, 1

ii. P(X = −3) = `5/6 xx 5/6 xx 5/6 = 125/216`

P(X = −1) = `5/6 xx 5/6 xx 1/6 = 25/216`

P(X = 0) = `5/6 xx 1/6 = 5/36`

P(X = 1) = `1/6`

Required probability distribution:

X	−3	−1	0	1
P(X)	`125/216`	`25/216`	`5/36`	`1/6`

iii. Expected value = `sumpx`

= `(−3)(125/216) + (-1)(25/216) + 0 + (1/6)`

= `-91/54`

= `-1 37/54 ≈ -1.69`