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Probability Distributions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsProbability Distributions1 Mark
Question
Let's return to the example in which $X$ has the following probability density function :
$f(x)=\frac{x^3}{4}$ for $0<x<4$. What is the cumulative distribution function $X$ ?
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Answer

$F(x)=\int_0^x f(x) d x=\int_0^x \frac{x^3}{4} d x=\frac{1}{4}\left[\frac{x^4}{4}\right]_0^x=\frac{1}{16}=\left[x^4-0\right]=\frac{x^4}{16}$

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