Question

In: Statistics and Probability

The random variable Y has an exponential distribution with probability density function (pdf) as follows: f(y)...

The random variable Y has an exponential distribution with probability density function (pdf)

as follows:

f(y) = λe−λy, y >0

= 0, otherwise

(i) Showing your workings, find P (Y > s|Y > t), for s ≥ t. [3]

(ii) Derive an expression for the conditional pdf of Y , conditional on that Y ≤ 200. [3]

N(t) is a Poisson process with rate λ

(iii) Find an expression for the Cumulative Distribution Function (CDF) of the waiting time until the first event. (Hint: Consider the probability of there being 0 events in time t.) [2]

(iv) Explain the relationship between the mean of the Poisson distribution with rate λ and the mean of the associated distribution for the waiting time.

Solutions

Expert Solution

here is the solution for this. I have used cumulative distribution function of exponential distribution to calculate probabilities of the type

P(X<a) =F(a) where F is cdf given below .

Please upvote If I am able to help you.

Thanks

orchestra answered 1 year ago
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