Transcription of SOLUTION FOR HOMEWORK 4, STAT 4351
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SOLUTION FOR HOMEWORK 4, STAT 4351
SOLUTION FOR HOMEWORK 4, STAT 4351 Welcome to your fourth HOMEWORK , which begins our study of chapter 3 and also the lastone before Exam 1. Here we are exploring basics of univariaterandom variables (rv): discreterv, continuous rv, pdf (probability density function), pmf(probability mass function), cdf(cumulative distribution function), calculation of let us look at your Problem A discrete random variableX:=X(w) is defined by its probability massfunction (in the text it is also referred to as the probability distribution but I prefer the pmfas less confusing)f(x),x X. HereXis the range of the random variableX(w) defined forw S. Please remember that bothfandXdefine the pmf of a discrete random variable.(a). Heref(x) = (x 2)/5 andx X={1,2,3,4,5}. Becausef(1) takes on negativevalue, it is not a valid pmf (see Theorem ).
must hold, we get 1+2+3+4+5 = 15 and this yields c = 1/15. Note(!): the same f(x) = cx but with x ∈ X = {1,2,3} is another pmf, because here the ... survivor (distribution) function of the rv X (in biostat/quality-control applications it is the probability that a patient/item will live/survive after time x).
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