Homework4Solutions_Final.pdf - STAT 225 Spring 2020...

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STAT 225 Spring 2020-- Homework 4------- -------Solutions All STUDENTSmust turn in via Blackboard by 11:59 pm on April 6, 2020. SHOW WORK!!!!!Full credit will not be given for answers only. NOTE: for any question asking you to determine a probability----you MUST write out a probability statement using proper notation!!!! Probabilities should be DECIMAL form and rounded to 4 decimal places. 1.For the following pdfs find the following (1) The value of ?that makes it a valid pdf. (2) The corresponding cdf. a)??(?) = {? ,0 ≤ ? ≤ 313? ,0 ,5 ≤ ? ≤ 8??ℎ???𝑖??(1)? ∫ ??30+13? ∫ ??85= 13? + ? = 1? = ?/?(2)??(?) ={0? ≤ 0?/40 < ? ≤ 33/4?−512+ 3/413 < ? ≤ 55 < ? ≤ 8? > 8b)??(?) = {?(? − 3)2,3 ≤ ? ≤ 90 , ??ℎ???𝑖??(1)? ∫(? − 3)2?? = 193Let ? = ? − 3then ?? = ??and change limits of integration ? ∫ ?2?? = 160?363= 1? =???(2)??(?) = {0? ≤ 31216(? − 3)33 < ? ≤ 91? > 9The middle part is found using u-substitution again. 172∫ (? − 3)2???3Let ? = ? − 3then ?? = ??and change limits of integration 172?2???−30=1216(? − 3)3
2.Suppose that a random variable, X, has a probability density function (pdf) given by ??(?) ={?64(? + 8) +14,−4 ≤ ? ≤ 019, 0 < ? ≤ 60 ,??ℎ???𝑖??a)Write out the CDF for this function--- i.e.write out ??(?).
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