math3C_Towsner_s11_midterm2.pdf

# The number of calls they receive is independent so

This preview shows pages 3–6. Sign up to view the full content.

distributed with mean 10, and therefore parameter 10. The number of calls they receive is independent, so the probability they both receive exactly 5 calls is P ( N X = 5 and N Y = 5 ) = P ( N X = 5 ) P ( N Y = 5 ) = e - 6 6 5 5 ! e - 10 10 5 5 ! 3 of 7

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

View Full Document
3. ( 20 points ) The average number of points scored in a game by a certain basketball team is 65. Assume that the number of points scored is Poisson distributed. ( a ) What is the standard deviation in the number of points scored? The parameter of the Poisson distribution is its mean, in this case 65. This is also the variance, so the standard deviation is 65. ( b ) What is the likelihood of this particular team scoring 75 points in a given game? e - 65 65 75 75 ! ( c ) What is the likelihood of this particular team scoring 10 points in a game? e - 65 65 10 10 ! ( d ) A smudge makes it hard to read score of the latest game: the team got either 70 points or 78 points. What is the likelihood that the team scored 78, given that the team scored either 70 or 78? P ( X = 78 | X = 78 or X = 70 ) = P ( X = 78 ) P ( X = 78 or X = 70 ) = P ( X = 78 ) P ( X = 78 ) + P ( X = 70 ) = e - 65 65 78 78 ! e - 65 65 78 78 ! + e - 65 65 70 70 ! 4 of 7
4. ( 30 points ) X is a random variable distributed according to the exponential distribution with parameter 2. Y is a random variable with pdf g ( x ) = 16 xe - 4 x if x > 0 0 if x 0 X and Y are independent. ( a ) For t 0, what is P ( X > t )? (Your answer should be a function of t .) This the exponential distribution, so the answer is 1 - F ( t ) where F is the cdf of X , so e - 2t ( b ) For t 0, what is P ( Y > t )? (Your answer should be a function of t .) R t g ( x ) dx = R t 16xe - 4x dx . We apply integration by parts with u = x v = - 4e - 4x du = dx dv = 16e - 4x dx so lim a →∞ Z a t 16xe - 4x dx = lim a →∞ - 4xe - 4x a

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

View Full Document
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