Discuss the below:
Q1: Cars arrive at a toll booth at a mean rate of 5 cars every 10 minute according to poisson process.Find the probabaility that the toll collector will have to wait longer than 26.30 minutes before collecting the eighth toll.
Q2: If 15 observations are taken independently from a chi-square distribution with four degrees of freedom, find the probability that at most 3 of the 15 observations exceed 7.779.
Q3: If 10 observations are taken independently from a chi-square distribution with 19 degrees of freedom, find the probability that exactly 2 of the 10 sample items exceed 30.14.
Q4: Cars arrive at a tool booth at a mean rate of five cars every 10 minutes according to a Poisson process. Find the probability that the toll collector will have to wait longer than 26.30 minutes before collecting the eighth toll.
Q5: In a medical experiment, a rat has been exposed to some radiation. The experimenters believe that the rat's survival time X ha s the p.d.f.
f(x) = 3x2 e-(x/120)3/1203 0
(a) What is te probability that the rat survives at least 10 weeks?
(b) Find the expected value of the survival time