# Lab2 - Statistics 103 Lab 2 5 Suppose X has the following...

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Statistics 103: Lab 2 LAB PROBLEMS 1. Suppose that your friend has a strange habit when eating M&M’s. He will continue eating M&M’s un- immediately stop. Let X your friend consumes in one sitting. If we assume PMF of X is p X ( x ) = ± x - 1 x - 3 ² 0 . 20 3 0 . 80 x - 3 where x = 3 , 4 , 5 ,... . What is the probability that snack? 2. Let W be a random random variable with PMF given by: p W ( w ) = . 7 if w = - 2 . 15 if w = 0 . 05 if w = 1 . 1 if w = 5 Find Pr ( W = 0 W = 1), Pr ( W = 0 W = 1) and Pr ( W < 1 | W 0) . 3. FIG. 1 shows the PMF of a random variable X . Find P ( X > . 7) 0.4 0.6 0.8 1 x p(x) FIG. 1. The above plot shows the PMF of a random variable X . 4. Consider a box that contains a bunch of tickets: each ticket has a 1 or 0 written on it. Let p denote the proportion of tickets with a 1 written on it. Now randomly pick a ticket from this box and let the number be denoted Y . Find P ( Y = 1), EY and SD ( Y ). 5. Suppose X has the following PMF: p X ( x ) = ( . 7 if x = - 2 . 3 if x = 0 Find the variance of X using the formula x ( x - EX ) 2 p X ( x ) and the formula E ( X 2 ) - ( EX ) 2 and comment which one is easier to use. 6. If EX = 1 and var( X ) = 2 . 5 ﬁnd EY where Y = (2 - X ) 2 . PRACTICE PROBLEMS 1. In the dice game Yahtzee, one objective is to roll ﬁve six-sided dice simultaneously and try to get them to all show the same number. Suppose that your friends allow you to continue rolling all ﬁve dice until all ﬁve dice match. Let X be the number of turns it takes you to roll ﬁve of the same number. The PMF of X is given by p X ( x ) = ± 6 4 - 1 6 4 ² x - 1 1 6 4 where x = 1 , 2 , 3 ,... . What is the probability that you can stop immediately after your 3rd roll? 2. The number of times a certain web server is ac- cessed per minute ( X ) can be modeled by the fol- lowing PMF. p X ( x ) = 2 . 5 x e - 2 . 5 x ! where x = 0 , 1 , 2 , 3 ,... . Calculate the probability that the web server is accessed at most once during any given minute.

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Lab2 - Statistics 103 Lab 2 5 Suppose X has the following...

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