Test 3 & Solutions

# Test 3 & Solutions - Probability and Statistics Course...

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Probability and Statistics, Course 92.386/407 Test 3 Time: 1 hour 30 minutes Please answer any five of the following six questions. Each question is worth 5 points Numerical answers without supporting statements will not be given credit, L If the time (in minutes) of a telephone conversation is a random variable Y with the 1 _l following distribution: fy(y) = je 5; y> 0, a Determine the variance and standard deviation ofY h, Find E (Y + 5f 2" The pdf of a random variable Y is given by f y(y) = e -Y; y> 0 a, Find the moment generating function, My(t), ofY. b. Use My(t) to find E (Y) and Var (Y), 1 (3) 3, Given that the random variable X has the probability distribution fx(x) ="8 x for x = 0, 1, 2, 3, find the moment generating function of X and use it to determine E (X) and Var(X) 4" An electronic switching device occasionally malfunctions and may need to be replaced" It is known that the device is satisfactory if it makes, on the average, no more than 0.2 errors per hour, A particular 5 hour "test" period is chosen to test the device.

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