1) Let X₁, X2, X3,... X be a sequence of independent and identically distributed with thefollowing probability density function((0+1)x-0-20,f(x; 0) = {if 1 < x < 0⁰otherwisea) Is f(x; 0) a member of one-parameter regular exponential family? If yes, writedown the functions, h(x), c(0), w(0) and t(x).b) Use method of moments to find a statistic that we can use to estimate theparameter 0.

Given that For given pdf we have to proof that it is a one parameter regular exponential family of…

Answered: 1) Let X₁, X₂, X3,... X be a sequence…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 4CR

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(1) Let X b(16,- 5,-) find E(4- 3x) and distribution function.
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4. "Time headway" In highway traffic flow the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point is called time headway. Now, let X = the time headway for two randomly chosen consecutive cars on a highway during a period of heavy traffic flow. The following probability density function of X is suggested by traffic experts: f(x) = 0.15*e-0.15(x-0.5) for (x ≥ 0.5 sec) 0 otherwise a. Draw f(x) from x = 0 to x= 10 sec. b. Find P(X ≤ 5 sec) and show it on the figure you have drawn. c. What is E[X] and Var[X] ? d. Find Cumulative Distribution Function of X.
A random variable X has probability density function (x² + 2x + 4) for 0 < x < 3 f(x) = otherwise. Which of the following gives the cumulative distribution function F(x)?

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