Question 3The following represents the time until the first occurrence of an earth quake in a certaingeographic location in months. Derive the maximum likelihood estimator of the unknown parameterbeta. Graph the histogram of the data, and compute the probability the time until the nextoccurrence/earth quake is less than 10 months.Data2, 1, 3, 18, 5, 4, 3, 12, 26, 1, 22, 5, 7, 15, 18..35.99.61.65.01

Answered: Image /qna-images/answer/b33e0726-def7-442d-aa74-7139d3068786.jpg

Answered: The following represents the time until…

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 number of days between precipitation events during the fall season is modeled by an exponential distribution with mean 9.7. Compute the probability that the next inter-arrival time for precipitation events is more than 7 days. Use three decimal place accuracy.
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:
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 batteryhas 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
If the power received at the MU is lognormal with standard deviation of 9dB, the outage probability can be expressed as erfc(x)/2. determine the value of x given the average power received is -97dBm and the threshold power is -101dBm.
The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 66 mg/mi. A company has 1616 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)
The time between failures of our video streaming service follows an exponential distribution with a mean of 40 days. Our servers have been running for 17 days, What is the probability that they will run for at least 97 days? (clarification: run for at least another 80 days given that they have been running 17 days). Report your answer to 3 decimal places.
The type of battery in Jim's laptop has a lifetime (in years) which follows a Weibull distribution with parameters a = 2 and B = 4. The type of battery in Jim's tablet has a lifetime (in years) which follows an exponential distribution with parameter A = 1/4. Find the probability that the lifetime of his laptop battery is less than 2.5 years and that the lifetime of his tablet battery is less than 3.2 years. (Answer as a decimal number, and round to 3 decimal places).
The lifespans of light bulbs are known to follow an exponential distribution. The exponential distribution, often denoted exp(β), is characterized by a single mean parameter β. The exponential distribution has a unique property that its standard deviation is equal to its mean. Suppose you order 100 light bulbs known to each have lifespans (in years) distributed according to exp(4). What is the probability that the average lifespan of your 100 light bulbs exceeds 5 years? (Using R it possible)
Assume that women's weights are normally distributed with a mean given by μ=143 lb and a standard deviation given by 29 lb.(a) If 1 woman is randomly selected, find the probabity that her weight is between 113 lb and 172 lb(b) If 3 women are randomly selected, find the probability that they have a mean weight between 113 lb and 172 lb(c) If 73 women are randomly selected, find the probability that they have a mean weight between 113 lb and 172 lb
The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.6 and B = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.7520 0.7520 0.1065 x X X (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 0.6312 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) 191 Xhr

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