Exercise 7: Suppose upon arriving at a bus stop, the number of minutes you have to wait for a bus to arriveis given by the probability density function:(c(10 – x)²,0,0

We are given the probability density function:

Answered: Exercise 7: Suppose upon arriving at a…

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 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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Do you dislike waiting in line? A supermarket chain has used computer simulation and information technology to reduce the average waiting time for customers at 2,300 stores. Using a new system, which allows the supermarket to better predict when shoppers will be checking out, the company was able to decrease average customer waiting time to just 28 seconds. (a)Assume that supermarket waiting times are exponentially distributed. Show the probability density function of waiting time at the supermarket. f(x) = x ≥ 0 elsewhere (b) What is the probability that a customer will have to wait between 30 and 45 seconds? (Round your answer to four decimal places.) (c) What is the probability that a customer will have to wait more than 2 minutes? (Round your answer to four decimal places.)
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[1] The probability density function of a random variable X is SC(x + 4), -4 4.

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Exercise 7: Suppose upon arriving at a bus stop, the number of minutes you have to wait for a bus to arrive is given by the probability density function: (c(10 – x)², 0, 0