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