Answered: You have a device that uses a single…

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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Please use excel formulas when possible:

You have a device that uses a single battery, and you
operate this device continuously, never turning it off.
Whenever a battery fails, you replace it with a brand new
one immediately. Suppose the lifetime of a typical battery
has an exponential distribution with mean 205 minutes.
Suppose you operate the device continuously for three
days, making battery changes when necessary. Find the
probability that you will observe at least 25 failures.
(Hint: The number of failures is Poisson distributed.)

In the previous problem, we ran the experiment for
a certain number of days and then asked about the number of failures. In this problem, we take a different
point of view. Suppose you operate the device, starting
with a new battery, until you have observed 25 battery
failures.

What is the probability that at least 15 of
these 25 batteries lived at least 3.5 hours? (Hint: Each
lifetime is exponentially distributed

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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