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Probability Distribution

A discrete ra...

Question

A discrete random variable $X$ , can take all possible integer values from $1$ to $K$ , each with a probability $1 / K$ . Its mean is

K

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K + 1

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K / 2

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K / 4

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Solution

The correct option is A $K$
Mean $= μ = \sum_{i = 1}^{K} x_{i} p_{i}$
$= 1 \times 1 + 2 \times \frac{1}{2} + 3 \times \frac{1}{3} + . . . . . K \times \frac{1}{K}$
$= 1 + 1 + . . . . u p t o K t i m e s$
Mean $μ = K$

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