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Unformatted text preview: s the value 5 20% of the time, the value 10 30% of the time and the value 8 50% of the time. Let X denote the number that occurs when you spin the spinner. Determine the mean and variance of X. 5. Suppose that X is the Poisson random variable that denotes the number of customers that enter a store in a given hour. Given that the mean of X is 4, (a). What is the probability that at least 2 customers enter the store in a given hour? Express you answer in terms of e. (b). Given that at most one customer entered the store, what is the probability that exactly one customer entered the store? 6. Suppose that there is a box of 20 Ping- Pong balls, each labeled with one of the numbers 1 – 20 (each number used once). Five balls are chosen with replacement. and we let X denote the sum of their labels. What is E(X)? Hint: Express X as a sum of other random variables 7. (a). Let X be a b(32,0.25) binomial random variable. Determine the value of E ( X 2 ) . (b). Suppose X is a geometric random variable and that P( X = 2 ) = 9 P ( X = 4) . What is P( X = 3) ? . (c). Suppose that X is a Poisson random variable with mean 4. Let Y = 5X + 3. What is the mean and variance of Y ?...
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This note was uploaded on 01/25/2014 for the course MATH 511 taught by Professor Sumner during the Spring '13 term at South Carolina.

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