Question 3 The exponential distribution is a probability distribution that describes the time needed for a process tochange state. Suppose the number of minutes you wait in line for lunch at the HUB has the probabilitydensity functionCe-¤/11x > 0p(x) = {x < 0(a) In order to be a probability density function, we require| p(a)1.dx =Use this to solve for the normalization constant C.(b) The probability that the wait time is between a and b minutes is given byp(x) dx. Find theprobability thati. you wait between 5 and 8 minutes for your lunch.ii. you wait at least 15 minutes for yourlunch.(c) The mean, or average, wait time is given byx =dx.-00Calculate the mean wait time for lunch at the HUB.(d) The median m wait time is defined by the equation| p(x) = 0.5.Calculate the median wait time.

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Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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A random variable X has a probability density function 0; x<0, f(x) = 0≤x≤ 1, ; 1
The exponential distribution is a probability distribution for non-negative real numbers. It is often used to model waiting or survival times. The version that we will look at has a probability density function of the form p(y|v) = exp(-e¯ºy — v) (1) where y R+, i.e., y can take on the values of non-negative real numbers. In this form it has one parameter: a log-scale parameter v. If a random variable follows an exponential distribution with log-scale v we say that Y~ Exp(v). If Y~ Exp(v), then E [Y] =e" and V [Y] = e²v. 1. Produce a plot of the exponential probability density function (1) for the values y E (0, 10), for v = 1, v = 0.5 and v= 2. Ensure the graph is readable, the axis are labeled appropriately and a legend is included. ta il 2. Imagine we are given a sample of n observations y = (y₁,..., yn). Write down the joint proba- bility of this sample of data, under the assumption that it came from an exponential distribution with log-scale parameter v (i.e., write down the…
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A company uses wood chips in the manufacture of processed wood pieces of various sizes. Suppose the tons of wood chips T used per day has a probability density function f(T) = 0.25e-0.25T (a) Find the probability of using more than 4 tons of wood chips in a day. (Round your answer to three decimal places.) (b) Find the number of tons 7 (to the nearest ton) so that the probability of using more than 7 tons in a day is 0.07. tons
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