# Exercise 3 a satellite system consists of n

• Notes
• 2

This preview shows pages 1–2. Sign up to view the full content.

EXERCISE 3 A satellite system consists of n components and functions on any given day if at least k of the n components function on that day. On a rainy day each of the components independently functions with probability p 1 , whereas on a dry day they independently function with probability p 2 . The probability of a rainy day is θ . a. Give an expression of the probability that the satellite system will function at any given day. b. Evaluate the above probability when n = 3, k = 1, p 1 = 0 . 85, p 2 = 0 . 90, and θ = 0 . 20. c. If the satellite system functioned yesterday what is the probabilty that it was a rainy day? Use n = 3, k = 1, p 1 = 0 . 85, p 2 = 0 . 90, and θ = 0 . 20. EXERCISE 4 Let X be a geometric random variable with probability of success p . a. Show that for a positive integer k , P ( X > k ) = (1 - p ) k . b. Show that P ( X > n + k - 1 | X > n - 1) = P ( X > k ) EXERCISE 5 Two boys play in the following way. They take turns shooting and stop when a basket is made. Player A goes first and has probability p 1 of making a basket on any throw. Player B , who shoots second, has probability p 2 of making a basket. The outcomes of succesive outcomes are assumed to be independent.

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern