{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Stat400Mid1_Prac_ans - Statistics 400 Mathematics 463...

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

View Full Document Right Arrow Icon
Statistics 400 / Mathematics 463 Practice Exam 1 (BL1) Spring 2012 Solutions 1. True or False (No need to explain) [8 points] (a) For a continuous random variable, the cumulative distribution function should be continuous. T (b) The quantity median is the same as mean. F (c) Two events A and B are independent if the conditional probability P ( A | B ) is same as P ( A ), provided that P ( B ) > 0. T (d) Event A and its complement A 0 are mutually exclusive and mutually exhaustive. T 2. [10 points] Suppose that E and F are two events such that P ( E ) = 0 . 7 and P ( F ) = 0 . 5. (a) [5 points] Prove that P ( E F ) 0 . 2. 1 P ( E F ) = P ( E )+ P ( F ) - P ( E F ) . Therefore P ( E F ) 0 . 7+0 . 5 - 1 = 0 . 2. (b) [5 points] Suppose we know P ( E F ) = 0 . 3, find out P ( E 0 | F ). P ( E 0 | F ) = P ( E 0 F ) P ( F ) = P ( F ) - P ( E F ) P ( F ) = 0 . 5 - 0 . 3 0 . 5 = 2 / 5 1
Image of page 1

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

View Full Document Right Arrow Icon
3. [10 points] Every day, Tom makes a return trip to campus either by bus, or by bike. If it is raining, he takes the bus with probability 0.9 and bikes with probability 0.1. If it is sunny, he takes the bus with probability 0.4, and bikes with probability 0.6. Suppose it rains with probability 0.15 and is sunny with probability 0.85. Define the following events for Tom’s travel to campus: A = { by bus } , B = { by bike } , R = { rainy } , S = { sunny } .
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern