Suppose you have the following random sample with n independent obser-vations:X1, X2,..., Xniid* Uniform(-0,0)(a)the minimum of the sample, denoted by X(1)·Find the cumulative distribution function and probability density function of(b)What does X(1) converge in probability to? Justify your answer.What does iAi converge in probability to? Justify your answer.(c)nX(1)

Answered: Image /qna-images/answer/b82186ac-703f-4ce3-a7f1-46c040024dc1.jpg

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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Suppose that the unknown X is uniformly distributed between 0 and 2. What is the expected value of (4X3 + 1)?
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Previously, De Anza's statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed with a mean of $0.88. Suppose that we randomly pick 25 daytime statistics students. Find the probability that an individual had between $0.80 and $1.00. Graph the situation, and shade in the area to be determined.
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A biased coin with probability q of landing heads is repeatedly tossed until the first head is seen. The number of tails X before the first head is modelled as a geometric distribution with probability mass function P(X = x) = g(1-q). The experiment was repeated n times and x1,x2,..., Xn tails were observed. (a) Write down the likelihood for q. Show that the maximum likelihood estimate for q is â = n n+S n where S = x₁. (b) Find the Fisher information and hence the asymptotic variance for â. (c) A Beta(ao,Bo) distribution is chosen as the prior distribution for q. Show that the posterior distribution is Beta(a₁,₁), where you should determine a₁ and ₁. (d) We have n = 5 and observed data x₁,...,x₂ = 4,2,5,6,3. (i) What is the maximum likelihood estimate â? (ii) Find an approximate 95% confidence interval for q. (iii) Before seeing the data, our probability distribution for q has mean 0.4 and standard deviation 0.2. Find values of ao and Bo corresponding to this belief. What is then the…
Let X₁, X2, Xn be a random sample from a population with cumulative distribution function F(x) = xº, 0 0. ...

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