Probability Density function of continuos random varaible

A continuous random variable has the probability density function

$\displaystyle

f_x(x) \; = \; \begin{cases} \frac{1}{b-a} \qquad , \qquad a< x<b \\
0 \qquad, \qquad otherwise
\end{cases}
$

i) Find the cumulative distribution function and sketch it
ii) Find E[X] and Var X.

Quote:

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Originally Posted by Stats

A continuous random variable has the probability density function

$\displaystyle

f_x(x) \; = \; \begin{cases} \frac{1}{b-a} \qquad , \qquad a< x<b \\
0 \qquad, \qquad otherwise
\end{cases}
$

i) Find the cumulative distribution function and sketch it
ii) Find E[X] and Var X.

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What have you tried ?

This is the uniform distributioN.