Suppose you have the following random sample with n independent obser-vations:X1, X2,.Uniform(0, 0)Xn....(a)Find the cumulative distribution function and probability density function ofthe maximum of the sample, denoted by X(n).Show that X(n) 2, 0.(b)(c)Let Xn denote the sample mean. What does2XnlogX (n)converge in probability to? Justify each step you make to get to the answer.

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Answered: Suppose you have the following random…

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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The lifetime of a machine part has a continuous distribution: Osx<40 fylx) = (10+ x)? else a. Calculate the probability that the lifetime of the machine part is more than 6. b. Calculate the expectation of life of this machine C. Calculate the variance Calculate the probability that the lifetime of the machine part is more than 4 given that is lasts for less than 12 d.
2..You are given fT(30)(t) = t/1250 0≤t<50 0 o.w. a) Find the probability that (30) dies between ages 40 and 45. b) Find the probability that (60) dies between ages 65 and 85. c) Define the cumulative distribution function of T (45). d) Define the force of mortality of T (50).
The random variable X has expected value E(X)=4 and Var(X)=4. Here, we want to approximate the probability that X lies in the interval [3.4,5.4] using a transformation to a standard normal distribution Z. Then we will need to calculate the probability that Z lies in the interval [z1,z2] where z1= z2= Suggest z1 and z2 Do NOT attempt to make any sort of continuity correction.

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