11. Let f(z) and F() denote, respectively, the PDF and the CDF (cumulative distributionfunction) of a random variable X. The conditional PDF of X given X > zo, where zo is a fixedmumber, is defined as f(r X > ro) = f(r)/ [1 – F (ro)], for r > I9, and zero elsewhere. Showthat, if F(ro) <1, then f (r X > ro) is a PDF of a random variable.

Given: X is a random variable with PDF as fx and CDF as Fx. The conditional PDF of X given X>x0…

Answered: 11. Let f(z) and F() denote,…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Similar questions

Let W₁ < W₂ < ... < Wn be the order statistics of n independent observations from a U(0, 1) distribution. (a) Find the pdf of W₁ and that of Wn. (b) Use the results of (a) to verify that E (W₁) = 1/(n+1) and E(Wn) = n/(n+1).
3 Let X be the number of siblings of WSU students. The pdf of X is: f(x) = (5-x)/15 for x = 0, 1, 2, 3, 4 What is the probability that a randomly selected student has 3 or more siblings if it is known that they are not an only child X 0.133 X 0.2 / 0.3 O X 0.667 X 0.933
3) Suppose X is a discrete variable that has the following pr function (pdf) f (X) 1. 0.40 0.20 3 0.15 4. 0.25 a) Calculate the cumulative distribution function (the b) Find the expected value, showing your work: E(X) c) Find the variance, showing your work: Var (X)
2. Let X₁,..., Xn be iid observations from a pdf defined by 0 f(x|0) = 0 0. (1+x)¹+0¹ Find a complete sufficient statistic.
Let random sample of n observations from each of the distributions: a. Poisson distribution with parameter θ. b. f(x, θ) = (1/ θ) e-x/θ , 0 < x. In each case find the Minimum Variance Estimator of θ and prove its efficiency.
(b) Let X₁, X₂, X3 be uncorrelated random variables, having the same variance ². Consider the linear transformations Y₁ = X₁ + X₂, Y₂ = X₁ + X3 and Y3 = X₂ + X3 . Find the correlations of Yi, Y; for i #j. (5 marks)
Let X1,..., Xn be a random sample from a uniform distribution on the interval [20, 0], where 0 0. Let X(1) < X(2) <...< X(n) be the order statistics of X1, ..., Xn.
Let X be a random variable with CDF x > 1 Fx(x) = 0 < x < 1 %3D x < 0 a. What kind of random variable is X: discrete, continuous, or mixed? b. Find the PDF of X, fx(x). c. Find E(ex).
2) Let X₁, X2, ..., Xn be a random sample from the pdf f(x;0) = 0xª−¹, 0≤x≤ 1,0 <0 < ∞. Find the MLE of 0 and show that its variance approaches 0 as n approaches ∞o.

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