fall08-quiz2

# fall08-quiz2 - PROBABILITY AND DECISION MAKING 45-730 REAL...

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PROBABILITY AND DECISION MAKING 45-730 REAL QUIZ 2 (OFFLINE) Problem 1 ( Expectation ) . Consider the following random variables: The random variable X takes the values { 0 , 1 , 2 } with equal probabilities. The random variable Y takes the value 9 with probability 1 3 and 12 with probability 2 3 . The random variable Z takes the values { 2 , 4 , 6 , 8 } with equal probabilities. (1.1) What is the expected value of X ? (1.2) What is the expected value of Y ? (1.3) What is the expected value of Z ? (1.4) What is the expected value of the random variable W = 2 X - Y + 4 Z ? Problem 2 ( Variance ) . Consider the following four random variables. A: Binomial random variable with parameters p = 1 2 ,n = 4. B: Poisson random variable with mean = 1. C: Discrete random variable which taking one of the values 0 , 1 , 2 , 3 , 4 with equal probabilities. D: Discrete random variable which takes value 0 with probability 1 2 and value 4 with probability 1 2 . (2.1) What is the variance of A ? (2.2) What is the variance of B ? (2.3) What is the variance of C ? (2.4) What is the variance of D ? Problem 3 ( ) . A vending machine sells snacks at \$0 . 90 each. Let X be the random variable representing the number of snacks sold per day. It is known that

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## fall08-quiz2 - PROBABILITY AND DECISION MAKING 45-730 REAL...

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