Question

The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous ran- dom variable with a cumulative distribution function ???? F(x)= 0, x<0, 1−e−4x, x≥0. Find the probability of waiting fewer than 12 minutes between successive speeders.

Answer 1

Answer: 0.5507

Explanation:

Given : The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable X with a cumulative distribution function

`F(x)= \begin{cases}0,& x<0 \\ 1-e^(-4x), & x\geq0\end{cases}\end{document}`

Since , the waiting time is in hours , then we can write 12 minutes as
`(12)/(60)` hour i.e.0.2 hour.

Now, the probability of waiting fewer than 12 minutes between successive speeders is given by :-

`P(X<0.2)=1-e^(-4(0.2))=1-e^(-0.8)\\\\=1- 0.449328964117=0.550671035883\approx0.5507`

Hence, the required probability = 0.5507