practice_final_prob_solutions

# practice_final_prob_solutions - SDS 321 Practice questions...

• Test Prep
• 5
• 100% (2) 2 out of 2 people found this document helpful

This preview shows pages 1–3. Sign up to view the full content.

SDS 321: Practice questions 1. How many unique combinations can you get by rearranging the letters MISSISSIPPI? 11 letters so 11! permutations. 4 Is, 4Ss, 2 Ps, so 11! / (4!4!2!) unique combinations. 2. On the first day of a non-leap-year, I put \$1 in a box. On the second day, I put \$2 in the box. On the third day, I put \$3 in. And so on. At the end of the year (365 days), how much money is in the box? The first day you put in \$1, the last day you put in \$365. The average of these two is 183. The average of the second and penultimate days is also 183. Etc. So, the total is 365 × 183 = \$66795. 3. Let X be a normal random variable with mean 3 and variance 1, and let Y be a normal random variable with mean 4 and variance 2. (a) What is the distribution of Z = X + Y ? Normal (7 , 3) (b) What is the probability that Z is between 6 and 8? P (6 Z 8) = P ( 6 - 7 3 Z - 7 3 8 - 7 3 ) = P ( - 0 . 577 Z - 7 3 0 . 577) = 0 . 44 (from standard normal tables) 4. I am waiting for a bus, that I know will arrive at some time between 1pm and 2pm, with all times being equally likely. It gets to 1:30, and the bus has still not arrived. What is the probability that it arrives before 1:40? 1/3 5. Let X be a continuous random variable with PDF f X ( x ) = ( 0 . 125 x + 0 . 125 - 1 x 3 0 otherwise What is the PDF of Z = | X | ? f Z ( z ) = ( 0 . 25 0 x 1 0 . 125 + 0 . 125 x 1 < x 3 6. Alice and Bob are playing rock-paper-scissors. If both Alice and Bob play the same hand, they play again. What is the expected number of turns before someone wins? The time until someone wins is a Geometric distribution with p = 2 / 3 (probability someone wins). The expected value of a geometric distribution is 1 /p = 3 / 2. So, the expected number of goes before someone wins is 1 / 2. 1

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

7. On a given day, a Poisson (100) number of insects fly through my yard. Using an appropriate approximation, what is the the probability that, over the month of May (31 days), the average number of insects is between 98 and 102? You may use the fact that a Poisson ( λ ) random variable has mean and variance λ .
This is the end of the preview. Sign up to access the rest of the document.
• Fall '14
• Probability theory, Conditional expectation, Geometric distribution, continuous random variable

{[ 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