{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

utf-8__STOCHPROC_001

utf-8__STOCHPROC_001 - P ROBLEMS FOR THE MIDDLE TERM EXAM[1...

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

View Full Document Right Arrow Icon
P ROBLEMS FOR THE MIDDLE TERM EXAM [1] Given three sets A, B, C . Use the Venn diagram to illustrate the following sets: A B C , A B B ( C \ ( A B )) . [2] Let a card be selected from two ordinary packs of 52 cards. Denote A = { the card is Diamonds or clubs } , B = { the card is a red suit one } , C = { the card is not a Heart Jack } . Compute the following probabilities: P ( A ) , P ( B C ) , P ( C | B ) [3] EX 1( 2 points) : What are a sample space, events an their probilitiy? Formulate axioms of probability ? Give an example ? EX 2 ( 2 points) : What is the conditional probability of an event A given E . When three events A i , i = 1 , 2 , 3 are independent ? Give an example of a sequence of dependent ( non-independent) events A i , i 3 such that each pair of its membrs are independent. EX 3 (2 points) : A pair of fair dice is tossed. We obtain the finite equiprobable Ω consisting of the 36 ordered pairs of numbers between 1 and 6 Ω = { (1 , 1) , (1 , 2) , · · · , (6 , 6) } . Let X assign to each point ( a, b ) in Ω the minimum of its numbers, i.e X ( a, b ) = min( a, b ). What is the image set of random variable
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
Image of page 2
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