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 ).(b). Heref(x) =x2/30,x X={0,1,2,3,4}. The function is nonnegative, and4 x=0x2/30 = [1 + 4 + 9 + 16]/30 = is a valid pmf. Please note that you can exclude{0}from the range ofX(w).
SOLUTION FOR HOMEWORK 4, STAT 4351 Welcome to your fourth homework, which begins our study of chapter 3 and also the last one before Exam 1. Here we are exploring basics of univariate random variables (rv): discrete
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