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Rashid [163]
3 years ago
11

If x has a continuous uniform distribution on the interval (0,5), what is the 25th percentile for x?

Mathematics
1 answer:
Natasha_Volkova [10]3 years ago
4 0
Given that X\sim\mathrm{Unif}(0,5), it has PDF

f_X(x)=\begin{cases}\dfrac15&\text{for }0\le x\l5\\\\0&\text{otherwise}\end{cases}

and thus CDF

F_X(x)=\mathbb P(X\le x)=\begin{cases}0&\text{for }x

The 25th percentile is the value X=k such that \mathbb P(X\le k)=0.25. We have

\mathbb P(X\le k)=\dfrac k5=0.25\implies k=1.25
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