a. Prudential Insurance Company provides a multiplicity of insurance policies. The probability that claims are made in any financial year is 0.04. A researcher randomly selects 500 policies. Assume, the claims follows a standard normal distribution, calculate the probability at most 30 claims are made in a financial year. b. Assume the claim in (a) is a random variable X that follows a Poisson distribution with a parameter μ. Answer the following questions: i. Write down the moment generating function Mx (t) ii. By differentiating M, (t), show that the mean and variance of X are both equal to H.
a. Prudential Insurance Company provides a multiplicity of insurance policies. The probability that claims are made in any financial year is 0.04. A researcher randomly selects 500 policies. Assume, the claims follows a standard normal distribution, calculate the probability at most 30 claims are made in a financial year. b. Assume the claim in (a) is a random variable X that follows a Poisson distribution with a parameter μ. Answer the following questions: i. Write down the moment generating function Mx (t) ii. By differentiating M, (t), show that the mean and variance of X are both equal to H.
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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Transcribed Image Text:a. Prudential Insurance Company provides a multiplicity of insurance policies. The
probability that claims are made in any financial year is 0.04. A researcher randomly
selects 500 policies. Assume, the claims follows a standard normal distribution, calculate
the probability at most 30 claims are made in a financial year.
b. Assume the claim in (a) is a random variable X that follows a Poisson distribution with a
parameter μ. Answer the following questions:
i.
ii.
Write down the moment generating function Mx (t)
By differentiating My(t), show that the mean and variance of X are both equal to
μ.
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Step 1: Write the given information.
VIEWStep 2: Determine the probability that at most 30 claims are made in a financial year.
VIEWStep 3: Determine the moment generating function.
VIEWStep 4: Determine the mean and variance of X by differentiating Mx(t).
VIEWStep 5: Determine the X by double differentiating Mx(t).
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