![]() However, if she can t sell them at $150, she won t sell them at all. The price of the tickets is $75, and the scalper will sell them at $150. A scalper is considering buying tickets for a particular game. (b) Calculate E by viewing X as a sum of random variables, whose mean is easily calculated. (a) Calculate E by first finding the PMF of X. Let X be the number of students that get an A in your class. The probability of an undergraduate (or graduate) student getting an A is 1/3 (or 1/2, respectively). Your probability class has 250 undergraduate students and 50 graduate students. If X and Y are the numbers of students that get an A and a B, respectively, calculate the joint PMF p X,Y. A class of n students takes a test in which each student gets an A with probability p, a B with probability q, and a grade below B with probability 1 p q, independently of any other student. Let L 1 be the number of losses before its first win, and let L 2 be the number of losses after its first win and before its second win. Its performance in each game is independent of its performance in other games. The MIT football team wins any one game with probability p, and loses it with probability 1 p. Joint PMFs of Multiple Random Variables Problem 12. Find the values of c and d that will make the following formula true: E = ce 2 + d ( E ) 2. Let X 1., X n be independent, identically distributed random variables with common mean and variance. Let N be a nonnegative integer-valued random variable. (d) Find E, assuming an infinite number of contestants. Let X be a discrete random variable that is uniformly distributed over the set of integers in the range, where a and b are integers with a n) as a function of n. What is the PMF of the total premium paid up to and including the year when the first claim is filed? SECTION 2.3. The probability that a claim is filed in a given year is 0.05, independently of preceding years. The annual premium of a special kind of insurance starts at $1000 and is reduced by 10% after each year where no claim has been filed. Show that approximately 649, 740 hands would have to be dealt in order that the probability of getting at least one royal flush is above 1 1/e. The probability of a royal flush in poker is p = 1/649, 740. Tsitsiklis C H A P T E R 2 : A D D I T I O N A L P R O B L E M S SECTION 2.2. 1 I N T R O D U C T I O N T O P R O B A B I L I T Y by Dimitri P. ![]()
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