Show that if a random variable has an exponentialdensity with the parameter θ, the probability that it willtake on a value less than −θ · ln(1 − p) is equal to p for 0 Fp < 1.

Solve all parts kindly in 30 mij and take a thumb up

The Exponential pdf for continuous random variable Y takes the form e-ylß y > 0 f(V) = for ß > 0. y 1.6) Give your answer to three decimal places.

According to the U.S. Customs and Border Protection Agency, the average airport wait time (time from arrival at the airport until the completion of security screening) at Chicago's O'Hare Inter- national airport is 32 minutes for a passenger arriving during the hours 4-5 PM. Assume the wait time is exponentially distributed so that p(t) = ke-kt for 0≤t<∞, where k is the reciprocal of the average wait time. Assume t is measured in minutes. 1. Sketch a labeled plot of the relevant pdf on the interval [0, 90] minutes (while remembering that it is defined for all t≥ 0.) 2. Set up integrals (you can write p(t) for the integrand) for the following probabilities: (a) Waiting longer than 60 minutes. (b) Waiting shorter than 30 minutes. (c) Waiting between 20 and 40 minutes. 3. Evaluate the probability that the waiting time is longer than 60 minutes (part 2(a) above) and convert to a percentage with two decimal places.