MATH 464 HOMEWORK 4 SPRING 2013 The following assignment is to be turned in on Thursday February 14 2013. 1. Let X be a discrete random variable on a probability space (;F; P). Let g : R ! R be a function and set Y = g(X) i.e. Y : ! R is dened by Y (!) = g(X(!)) for all ! 2 : Prove that Y is a discrete random variable. 2. Let 0
MATH 464 HOMEWORK 4 SPRING 2013 The following assignment is to be turned in on Thursday February 14 2013. 1. Let X be a discrete random variable on a probability space (;F; P). Let g : R ! R be a function and set Y = g(X) i.e. Y : ! R is dened by Y (!) = g(X(!)) for all ! 2 : Prove that Y is a discrete random variable. 2. Let 0 0. Compute the following: a) P(2 X 4) b) P(X 5) c) P(X is even) give each answer in exact form and with the choice of = 2 give a decimal approximation to the above which is accurate to 3 decimal places. 4. Let X be a discrete random variable whose range is f0; 1; 2; 3; g. Prove that E(X) = 1Xk=0 P(X > k) : 5. Compute the expected value of the geometric random variable with pa- rameter 0 0 an integer. For any 0 k n denote by Pk = P(X = k). Compute 1
2 SPRING 2013 the ratio Pk??1 Pk for 1 k n : Show that this ratio is less than one if and only if k 0. Let g : R ! R be the function g(x) = x(x ?? 1). Set Y = g(X). Find E(Y ). 8. Let X be a function whose range is f1; 2; 3; g. Consider the values P(X = n) = 1 n(n + 1) for any n 1 : Does this function X dene a discrete random variable? If so what is E(X)?
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BENCHMARK – EFFECTS OF CHILDHOOD TRAUMA WORKSHEET
Academic Level University Subject Healthcare Type of Paper Other (Not listed) Paper Format APA Assessment Traits Benchmark Requires Lopeswrite Assessment Description Complete the “Effects of Childhood Trauma Worksheet” document attached. While APA format is not Read more…