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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.

Here f(x) = x2/30, x ∈ X = {0,1,2,3,4}. The function is nonnegative, and X4 x=0 x2/30 = [1 +4+9+16]/30 = 1. This is a valid pmf. Please note that you can exclude {0} from the range of X(w). ... (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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