MA2222 - HW01

MA2222 - HW01 - 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 4.7-1 MA2222 HW01 If X is a random variable with mean 33 and variance 16, use Chebyshev's inequality to find: (a) A lower bound for W{ {. { . . . # . . {$ '{ # - {4 . # (b) An upper bound for W{ . {I . 4 # {% '{ % {3 % # 4 {. # 4.7-2 If { { and (a) A lower bound for W{ $ {I $ { . { {I{{$ . . # , use Chebyshev's inequality to determine: I {. %% . %% % . . {$ %%%{ # (b) An upper bound for W{ . # # {' %%%{ % 4 {. 4.7-4 If Y is { (a) $ {, give a lower bound for W } . } % when: JJ JJJ }#"" . # . . (b) $ } . # { % 7 { I %{ . {# . }'"" . JJ JJJ % } . % 7 { % I % { Willis Thai % MA2222 HW01 . (c) $ # . {% ' # { % . . }'"" . # JJ JJJ % } . # "{ % 7 { % % I % { . {' " 4.7-6 Let be the mean of a random sample size of from a distribution with mean and variance . Use Chehbyshev's inequality to find a lower bound for W{ % {. I . . I % . . {$ '{ # 4 - . # 4 . # . . 5.2-1 # " #' % {, find: If Z is W{ (a) W{ I3 { { . { { { %% . % % (b) W{. 3 { { . - { %{ { % . % (c) W{ 2 . { { { . {I 3 . . - { % (d) W{ 2 %%{ . {I 3 %%{ . { %%{ . %%% (e) W{ % { { % {. { % { . % (f) W{ { { % {. { { . % (g) W{ { { % {. { { . % (h) W{ { {. { %%% { . { %% % % Willis Thai 5.2-7 MA2222 HW01 If X is normally distributed with a mean of 6 and a variance of 25, find: (a) W{ I3 { { { { { . { { I %% % . % % (b) W{ 3 3 { {. { { { . - { { 3I3 . - %% % (c) W{. I3 { {. I 3 . { { { . { { % . %% % (d) W{ 2 { . {I 3 { . { { . %%% (e) W{ . { {. { { % {. I { { . % (f) W{ . { {. { { % {. I { { . % (g) W{ . { {. { { %%% { . I { { . %% (h) W{ . { {. % { %% { . I % { { % { . %% % X , where Y is {. I { . { 5.2-22 The strength X of a certain material is such that its distribution is found by {. Find the distribution function and pdf of X and compute W{ W{ NOTE: The random variable X is said to have a lognormal distribution. { { { { { {I 3 { { { { 3 { #"{ $ { 3 { { #"{ $ I % . { { %% { . { . { . { 5.2-25 Assume that the fill X of a filling machine for a beverage has a normal distribution with and , measured in fluid ounces. (a) Compute W{ {. . {I 3 . { {. { {I { F . { { % I3 (b) In 50 independent such measurements, compute the probability that at least one is less than 12 ounces. ...
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