MA2212 - HW05

MA2212 - HW05 - Department of Mathematics Name Poly ID...

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Unformatted text preview: Department of Mathematics Name: ________________________________ Poly ID: _______________________________ Instructor's Name: _______________________ Course No:_____________________________ Course Section: _________________________ Homework Section No: ___________________ Willis Thai 2.5-3 MA2212 HW05 If the moment-generating function of X is {Y{ find the mean, variance, and pmf of X. H { { H { { $ XY - X Y - X Y - $ H { { - - $ - % % % H { { . {H { {{$ { { 2.5-21 Given a random permutation for the integers in the set {1, 2, 3, 4, 5}, let X equal the number of integers that are in their natural position. The moment generating function of X is {Y{ H { { % XY ' ' X Y- X Y- X Y (a) Find the mean and variance of X. H { { $ H { { H { { . {H { {{$ (b) Find the probability that at least one integer is in its natural position. {I 4 { . {I { . - % $ $ - % % - (c) Draw a graph of the probability histogram of the pmf of X. Willis Thai 2.6-3 MA2212 HW05 Customers arrive at a travel agency at a mean rate of 11 per hour. Assuming that the number of arrivals per hour has a Poisson distribution, find the probability that more than 10 customers arrive in a given hour. {I 2 { . {I 3 { 2.6-5 Flaws in a certain type of drapery material appear on the average of one in 150 square feet. If we assume the Poisson distribution, find the probability of at most one flaw in 225 square feet. {I 3 { #' " - #' # % 2.6-16 While testing a used computer tape for bad records, a computer operator counted the number of flaws per 100 feet of tape. Let X equal this random variable. Given that 40 observations of X yielded 5 zeros, 7 ones, 12 twos, 9 threes, 5 fours, 1 five, and 1 six. (a) Construct a relative frequency histogram and superimpose a Poisson pmf with { { { { ' &" &" #$ &" &" ' &" # &" # &" . {I {I {I {I {I {I {I { { { { { { { % % % % { { { { { { { { { { (b) Does the Poisson distribution seem to be a possible probability model for this experiment? , are close. Yes. Because the sample mean, , and the sample variance, J $ ...
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