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Let X ~ beta(alpha, beta). Find the population mode of X for alpha > 1 and...

Let X ~ beta(alpha, beta). Find the population mode of X for alpha > 1 and beta > 1.

Math   Statistics-And-Probability   
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Answer #1

Here,

So,

Equating this to 0, we get, -----(1)

Again differentiating with respect to 'x', we get,

Putting the value of 'x' from (1), we get,

Since this is less than 0, so f(x) is maximum at 'x' and thus, is the mode for X.

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