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homework08 - X b Find the second moment E X 2 c Find the...

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Probability for Engineering Applications Assignment #8, due at the beginning of class on Thursday, March 23 rd , 2006 1. (2 pts) (Textbook exercise 3.67) Find the mean and variance of the Poisson random variable with parameter α . 2. (2 pts) (Textbook exercise 3.74) Let Y = A cos( ωt )+ c where A has mean m and variance σ 2 and ω and c are constants. Find the mean and variance of Y . 3. (2 pts) (Textbook exercise 3.76) Let Y = ba X where a and b are positive constants and X is a Poisson random variable with parameter α . Find E [ Y ]. 4. (2 pts) The probability density function of the random variable X is f X ( x ) = ( 3 x 2 2 - 1 x 1 0 otherwise a. Find the expected value E
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Unformatted text preview: X ]. b. Find the second moment E [ X 2 ]. c. Find the variance var[ X ]. d. Find the standard deviation σ . 5. (2 pts) The probability that a telephone call lasts no more that t minutes is often modeled using the following exponential CDF: F T ( t ) = ( 1-e-t 3 t ≥ otherwise Find the probability that a call duration is within ± 1 standard deviation of the expected call duration? (Hint: if E [ T ] is the expected value of t and σ is the standard deviation of t , ±nd the probability P [ E [ T ]-σ ≤ t ≤ E [ T ] + σ ].) 1...
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