A RV X is exponentially distributed with parameter 1. Use Tchebycheff'sinequality to show that P(-1

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Answered: A RV X is exponentially distributed…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The arrival of an item ordered in Amazon is assumed to follow the exponential distribution with parameter λ. On average, the item is expected to arrive in 2 days. Calculate λ. What is the probability that you will receive the item within the first 24 hours? What is the probability that the item will arrive late after 5 days?
Today, the waves are crashing onto the beach every 4.4 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.4 seconds. Round to 4 decimal places where possible. The probability that the wave will crash onto the beach between 1.2 and 2.1 seconds after the person arrives is P(1.2 < x < 2.1) = The probability that it will take longer than 3.28 seconds for the wave to crash onto the beach after the person arrives is P(x > 3.28) = Suppose that the person has already been standing at the shoreline for 0.7 seconds without a wave crashing in. Find the probability that it will take between 3 and 3.7 seconds for the wave to crash onto the shoreline. 62% of the time a person will wait at least how long before the wave crashes in? seconds. Find the minimum for the upper quartile. seconds. Hint:
Let X have an exponential distribution with 0-1. The probability P 6. <5is equal to
The "kernel trick" is a quick way to integrate when you can recognize a distribution in some equation g(x) which you want to integrate. It takes advantage of the fact that the pdf f(x) of a proper probability distribution must integrate to 1 over the support. Thus if we can manipulate an equation g(x) into the pdf of a known distribution and some multiplying constant c in other words, g(x) = c · f(x) --- then we know that C • --- Saex 9(x)dx = c Smex f(x)dx = c ·1 = c Steps: 1. manipulate equation so that you can recognize the kernel of a distribution (the terms involving x); 2. use the distribution to figure out the normalizing constant; 3. multiply and divide by the distribution's normalizing constant, and rearrange so that inside the integral is the pdf of the new distribution, and outside are the constant terms 4. integrate over the support. The following questions will be much easier if you use the kernel trick, so this question is intended to give you basic practice. QUESTION:…
Please answer only the Determine the cumulative distribution function for the distribution, x such that P (X<x) 0.90 and Find the cumulative distribution. thank you!
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Show that the expectation of the exponential distribution with param- eter A is 1/A.
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The time (in minutes) between arrivals of customers to a post office is to be modelled by the Exponential distribution with mean 0.62. a) find the P(10<x<15) (10 and 15 are seconds) b) find the P(x>15| x>10) (10 and 15 are seconds) c) find the P(x<15) (15 is seconds)

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A RV X is exponentially distributed with parameter 1. Use Tchebycheff's inequality to show that P(-1 3/4. Find the actual probability also. For an exponential distribution with parameter 1, E(X) = – :글 and Var(X) %3D 22