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

Step-by-step 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 $\dfrac{12}{60}$ 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