Question

The cumulative distribution for a random variable x is

F(x) = 1/2 sqrt x-1; 1≤x≤5

Calculate the probabilities

Pr(1≤x≤4.1)

Answer 1

Given the cumulative distribution,

$F(x)=1/2(\sqrt{x-1})$, we can determine the $p(1\leqslant x\leqslant 4.1)$ as follows.

$p(1\leqslant x\leqslant4.1)=F(4.1)-F(1)$

Now,

$F(4.1)=(\sqrt{4.1-1})/2=\sqrt{3.1}/2=0.88034084$ and $F(1)=(\sqrt{1-1})/2=0$

Therefore,

$p(1\leqslant x\leqslant4.1)=F(4.1)-F(1)=0.88034084-0=0.88034084$

Thus, $pr(1\leqslant x\leqslant 4.1)=0.8803(4dp)$