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Question
The probability distribution of a discrete random variable X is given as under:
| X | 1 | 2 | 4 | 2A | 3A | 5A |
| P(X) | `1/2` | `1/5` | `3/25` | `1/10` | `1/25` | `1/25` |
Calculate: The value of A if E(X) = 2.94
Solution
We know that: E(X) = `sum_("i" = 1)^"n" "P"_"i""X"_"i"`
∴ E(X) = `1 xx 1/2 + 2 xx 1/5 + 4 xx 3/25 + 2"A" xx 1/10 + 3"A" xx 1/25 + 5"A" xx 1/25`
2.94 = `1/2 + 2/5 + 12/25 + "A"/5 + (3"A")/25 + "A"/5`
⇒ 2.94 = `0.5 + 0.4 + 0.48 + (13"A")/25 = 1.38 + (13'A")/25`
⇒ 2.94 – 1.38 = `(13"A")/25`
⇒ 1.56 = `(13"A")/25`
⇒ A = `(1.56 xx 25)/13` = 0.12 × 25
∴ A = 3
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