Question

If $X$ has the discrete uniform distribution $f(x)=\frac{1}{k}$ for $x=1,2, \ldots, k$, show that (a) its mean is $\mu=\frac{k+1}{2} ;$ (b) its variance is $\sigma^{2}=\frac{k^{2}-1}{12}$.

          If $X$ has the discrete uniform distribution $f(x)=\frac{1}{k}$ for $x=1,2, \ldots, k$, show that
(a) its mean is $\mu=\frac{k+1}{2} ;$
(b) its variance is $\sigma^{2}=\frac{k^{2}-1}{12}$.

Added by Beatriz O.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

02/19/2023

Step 1

The random variable $ X $ has a discrete uniform distribution over the integers $ 1, 2, \ldots, k $. This means that each of these $ k $ values is equally likely, with probability $ f(x) = \frac{1}{k} $. Show more…

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If $X$ has the discrete uniform distribution $f(x)=\frac{1}{k}$ for $x=1,2, \ldots, k$, show that (a) its mean is $\mu=\frac{k+1}{2} ;$ (b) its variance is $\sigma^{2}=\frac{k^{2}-1}{12}$.