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19/01/2022 4:51 pm
Topic starter
The probability distribution of random variable X is given by:
X → 1 - 2 - 3 - 4 - 5
P(X) → K - 2K - 2K - 3K - K
Let p = P(1 < X < 4 | X < 3). If 5p = λK, then λ equal to ________.
1 Answer
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19/01/2022 4:57 pm
ΣP(X) = 1 ⇒ k + 2k + 2k + 3k + k = 1
⇒ k = \(\frac{1}{9}\)
Now, p = P\(\Big(\frac{kX < 4}{X < 3}\Big)\)
= \(\frac{P(X = 2)}{P(X<3)}\) = \(\frac{\frac{2k}{9k}}{\frac{k}{9k} + \frac{2k}{9k}}\) = \(\frac{2}{3}\)
⇒ p = \(\frac{2}{3}\)
Now, 5p = λK
⇒ (5)\((\frac{2}{3})\) = λ\((\frac{1}{9})\)
⇒ λ = 30