A certain type of tree has seedlings randomly dispersed in a large area, with the mean densityof seedlings being approximately three per square yard. If the seedlings are randomly dispersed,the number of seedlings per region, Y can be modelled as a Poisson random variable. If a1forester randomly locates ten 1-square-yard sampling regions in the area, the probability thatnone of the regions will contain seedlings is 0.0498.2.3.1 If the seedlings really are randomly dispersed, the number of seedlings per region,Y, can be modelled as a Poisson random variable with 2 = 3. Interpret 1 =3.2.3.2 State the moment generating function_of the random variable Y.

Answered: Image /qna-images/answer/f412ad4c-f8e1-4534-babc-3af7af0a4a9c.jpg

Answered: forester randomly locates ten…

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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We roll a die 72 times. Approximate the probability of getting exactly 3 sixes with both the normal and the Poisson approximation and compare the results with the exact probability 0.000949681.
Cars arrive at a tollbooth at a mean rate of 36 cars every 9 minutes according to a Poisson process. Let X = the waiting time in minutes until the second toll is collected. a. How is X distributed?b. Write the complete pdf of X. c. What is the probability that the tollbooth collector has to wait less than 2 minutes to collect the second toll? d. Find the mean and variance of X.
What is Pr(X = n) for a Poisson random variable with parameter l? What is E(X ) in this case?
You decide to play K number of video games, where K is a Poisson random variable with parameter d. Assume that time you spend on a video game k = 1,2,..., K has a normal distribution with mean 4, and variance of. Also assume that 4k >> 0 and of is small, so that you can neglect negative time values. Let T be the total time you spend on playing video games, compute the mean and variance of T.
You decide to play K number of video games, where K is a Poisson random variable with parameter A. Assume that time you spend on a video game k = 1, 2,..., K has a normal distribution with mean µg and variance of. Also assume that µk >> 0 and of is small, so that you can neglect negative time values. Let T be the total time you spend on playing video games, compute the mean and variance of T.
8% of all cars fail the emissions inspection, find the probability that in a sample of 85 cars, 11 will fail. Use the Poisson approximation to Find the mean number λ of cars that fail the emissions inspection in a sample of 85 cars.
[Joint PDFS will be covered in Week 7] Let the random variables X and Y be the portions of the time in a day that two alternative routes between Topkapi and Uskudar have congestion (X for Route 1 and Y for Route 2). The joint PDF is given by fxy(x.y) = 2x2 + y? where Osxys1. (b) Assume Z=X+Y and W= XY and traffic experts are interested in the expected values of Z and W. E(Z) = and E(W) =O (Simplify your answers. Do not convert fractions into decimals.) (c) Find the variances of X and Y as well as the covariance between them. v(X) =D VY) =D and Cov(X, Y) =D (Simplify your answers. Do not convert fractions into decimals.) (d) The variance of Z can be found as V(Z) =- (Simplify your answer. Do not convert fractions into decimals.)
The number of times that a person contracts a cold in a given year is a Poisson random variable with parameter λ=5. Suppose that a new wonder drug (based on large quantities of vitamin C) has just been marketed that reduces the Poisson parameter to λ=3 for 70 percent of the population. For the other 30 percent of the population, the drug has no appreciable effect on colds. If Peter tried the drug for a year and has 3 colds in that time, what is the probability that the drug is beneficial for him?
Assume a normally distributed population of resting heart rates with μ = 76 and σ = 5. Compute the z-score for a heart rate of 73. What is the probability of randomly selecting someone whose heart rate is below 73? What is the probability of randomly selecting someone whose heart rate above 79? What is the probability of randomly selecting someone whose heart rate either below 60 or above 90?
Suppose that the time. in days, required to repair a heat pump is a random variable X having a gamma distribution with parameters k = 8 and A = 2. What is the probability that on the next service call (a) at most 3 day will be required to repair the heat pump? (b) at least 2 days will be required to repair the heat pump? %3D %3D
Question 5 Find the 82 -th percentile for a uniform random variable U with the lower limit 17 and the upper limit 21. The 82 -th percentile for U is (Round the answer to 2 decimal places)
The amount of time a cashier spends cashing out each customer at a store is modeled by an exponential random variable with parameter λ =1/3 minutes. Assume that the time the cashier spends with each customer is independent and identically distributed. Approximate the probability that the cashier will spend more than sixty minutes cashing out a total of eighteen customers. You may leave your solution as a real number rounded to fourdecimal places or you may leave your solution in terms of the standard normal CDF, Φ.

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