An investment firm offers its clients municipal bonds that mature after several years. Since the cumulative distribution function of T the number of years to maturity of a randomly chosen bond, is img Calculate the following probabilities P(T>3)= ? P(1.4

An investment firm offers its clients municipal bonds that mature after several years. Since the cumulative distribution function of T the number of years to maturity of a randomly chosen bond, is img Calculate the following probabilities P(T>3)= ? P(1.4

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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Consider an auto insurance portfolio where the number of accidents follows a Poisson distribution with parameter λ= 1000. Suppose the damage sizes for separate accidents are i.i.d. (independent identically distributed) r.v.'s having an exponential distribution with a mean of $2500. Each policy involves a deductible of $500. Let N₁ be the number of accidents that result in claims, and N₂ be the number of accidents that do not result in claims. Answer the following questions 1-5. Q1 Are N₁, N₂ dependent? Q2 Depends on a situation, No Yes What is the name of the distributions of N₁, №₂? O Marked Poisson Gamma Exponential Compound Poisson
Example 10: P and Q two securities, with expected returns of 15% and 24% respectively, and standard deviation of 35% and 52% respectively. Calculate the standard deviation of a portfolio weighted equally between the two securities if their correlation is -0.9.
The useful life of Johnson rods for use in a particular vehicle follows an exponential distribution with an average useful life of 5.2 years.You have a three-year warranty on your vehicle’s Johnson rod. What is the probability that the Johnson rod doesn’t fail before then? That is, what is the probability that its useful life doesn’t end before three years?b.If the vehicle manufacturer wants to limit the number of claims on the three-year warranty to 20%, what should the average useful life of the Johnson rod be?
Please answer exercise 2
Exercise 1. The annual number of murders in Chicago and LA are modeled as independent Poissons with means 500 and 240. [Note: The rates per 100,000 were about 23.8 and 7.3, resp, in 2016.] (a) What is the probability that Chicago sees over 525 murders next year [an increase of over 5%]? (b) What is the probability that LA sees over 252 murders next year [an increase of over 5%]? (c) What is the probability that Chicago and LA combined see a total of over 777 murders next year [an increase of over 5%]?
Example 12: The following are the different state of economy, the probability of occurrence of that state and the expected rate of return from security A and B in these different states: Rate of Return State Probability Security A Security B Recession 0-20 - 0:15 0-20 Normal 0.50 0-20 ()-30 Boom 0-30 0.60 0.40 Find out the expected returns and the standard deviations for these two securities. Suppose, an iuvestor has 20,000 to invest. He invests 15,000 in security A and balance in security B, what will be the expected return and the standard deviation of the portfolio?
Suppose a neighborhood grocery store buys 5 containers of skim milk at the wholesale price of $11 per container and sells it for $22 per container. After the expiration date, unsold milk is removed from the shelves and the grocer receives a credit from the distributor equal to three-fourths of the wholesale price. If the probability distribution of the variable is X and the number of containers sold from this lot is x f(x) 0 1/15 1 2/15 2 2/15 3 3/15 4 4/15 5 3/15 Calculate the expected utility. (Round to two decimal places)
The following table is a partial probability distribution for the MRA Company's projected profits (x = profit in $1,000s) for the first year of operation (the negative value denotes a loss). x f(x) −100 0.100 0.2050 0.30100 0.25150 0.10200 (a) What is the proper value for f(200)? f(200) = What is your interpretation of this value? This is the ---Select--- percent probability that the MRA will have a $200,000 profit. (b) What is the probability that MRA will be profitable? (c) What is the probability that MRA will make at least $100,000? Please only correct and with concept and dont do handwritten or skip please!!
Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…
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