Given the probability density function (p.d.f.) of the random variable $X$ as $f(x) = \frac{1}{2a}$ for $0 < x < 2a$ and $f(x) = 0$ otherwise, where $a > 0$, which of the following is correct?
- A$P(X < a/2) = P(X > a/2)$
- B$P(X < a/2) < P(X > 3a/2)$
- C$P(X < a/2) > P(X > 3a/2)$
- D$P(X < a/2) = P(X > 3a/2)$
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In a meeting,$60 \%$ of the members favour and $40 \%$ oppose a certain proposal. $A$ member is selected at random. We define a random variable $X$ such that $X=0$ if the member opposes the proposal and $X=1$ if the member is in favour. Then,$\text{Var}(X) = $
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|---|---|---|---|
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MediumKCET 2024
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