IE 255 Problem Set 4 - What need the capacity of the tank...

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Bogazici University Department of Industrial Engineering Fall 07, Probability for IE, IE 255 Problem Set #4 1) A school class of 120 students are driven in 3 buses to a symphonic performance. There are 36 students in one of the buses, 40 in another, and 44 in the third bus. When the busses arrive, one of the 120 students is randomly chosen. Let X denote the number of students on the bus of that randomly chosen student, and find E[X]. 2) Show that for a nonnegative random variable Y, 3) Let X be a random variable having expected value a and variance b 2 . Find the expected value and variance of Y= (X-a)/b 4) A filling station is supplied with gasoline once per week. If its weekly volume of sales in thousands of gallons is a random variable with probability density function
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Unformatted text preview: What need the capacity of the tank be so that the p robability of the supply’s being exhausted in a given week is 0.01? 5) It is known that E[X] = 0.6 , also the density function of X is given by the following. Find a and b 6) A miner is trapped in a mine containing three doors. The first door leads to a tunnel that takes him safety after two hours of travel. The second door leads to a tunnel that returns him to the mine after three hours of travel. The third door leads to a tunnel that returns him to his mine after five hours. If the miner is at all times equally likely to choose any one of the doors, what is the expected length of time until the miner reaches safety?...
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