# Density Function and CDF of a Uniform Random Variable [closed]

Suppose a random variable is equally likely to fall anywhere in the interval $[a,b]$.

Then the PDF is of the form:

$$f_{X}\left(x\right)=\begin{cases} \frac{1}{b-a} & \text{if }a\leq x\leq b\\ 0 & \text{otherwise}\end{cases}$$

Find and sketch the corresponding CDF. plzz help how I can find this in detail description..

## closed as off-topic by Did, drhab, Claude Leibovici, Cameron Williams, user228113 Oct 15 '16 at 23:38

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• Apply $F_X(x)=\int^x_{-\infty} f_X(y)dy$ discerning the cases $x<a$,$a\leq x<b$ and $b\leq x$. – drhab Oct 15 '16 at 7:18
• You might want to try the title "Mathematics" one day... – Did Oct 15 '16 at 7:22

Comment. Following the suggestion of @drhab: For the case $a = 2$ and $b = 4,$ here are plots of the density function $f(x)$ (at left) and the cumulative distribution function $F(x).$