In finance, one example of a derivative is a financial asset whose value is determined (derived) from a bundle of various assets, such as mortgages. Suppose a randomly selected mortgage in a certain bundle has a probability of 0.04 ofdefault. Complete parts a to d below.(a) What is the probability that a randomly selected mortgage will not default (that is, pay off)?The probability is(Type an integer or a decimal. Do not round.)(b) What is the probability that a bundle of five randomly selected mortgages will not default assuming the likelihood any one mortgage being paid off is independent of the others? Note: A derivative might be an investment that only pays whenall five mortgages do not default.The probability is(Round to four decimal places as needed.)(c) What is the probability that the derivative from part (b) becomes worthless? That is, at least one of the mortgages defaults.The probability is.(Round to four decimal places as needed.)(d) In part (b), we made the assumption that the likelihood of default is independent. Is this a reasonable assumption? Explain.V national economic conditions (such as recession)V impact all mortgages. So, if one mortgage defaults, the likelihood of a second mortgage defaulting

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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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If X is exponentially distributed, prove that the probability that X exceed its expected value is less than 0.5
3. [From Meyer 1970] The following (somewhat simple-minded) weather forecasting is used by an amateur forecaster. Each day is classified as "wet" or "dry" and the probability that any given day is the same as the preceding one is assumed to be a constant p (0 < p < 1). Based on past records, it is supposed that January 1 has a probability of B of being "dry." Letting Br=probability (that the nth day of the year is "dry"), obtain an expression for Bn in terms of B and p. Also evaluate lim Bn and interpret your results.
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Let Y denote the present value of a ten-year deferred 30-year temporary life annuity- immediate on (30). If i = 0 and mortality is uniformly distributed with w = = 100, calculate the probability that the sum of the payments will exceed E(Y).
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The graph of the discrete probability to the right represents the number of live births by a mother 51 to 56 years old who had a live birth in 2015. Complete parts (a) through (d) below. (...) 0.30- 0.25- 0.20- 0.15- 0.10- 0.05- 0.00 0.233 Ó 1 0.288 2 0.169 0.113 0.097 0.026 0.029 0.045 6 3 4 5 Number of Live Births 7 (a) What is the probability that a randomly selected 51- to 56-year-old mother who had a live birth in 2015 has had her fourth live birth in that year? 0.113 (Type an integer or a decimal.) (b) What is the probability that a randomly selected 51- to 56-year-old mother who had a live birth in 2015 has had her fourth or fifth live birth in that year? 0.21 (Type an integer or a decimal.) What is the probability that a randomly selected 51- to 56-year-old mother who had a live birth in 2015 has had her sixth or more live birth in that year? 0.1 (Type an integer or a decimal.) (d) If a 51- to 56-year-old mother who had a live birth in 2015 is randomly selected, how many live…
Q.#3 (a) In a certain industrial facility, accidents occur infrequently. It is known that the probability of an accident on any given day is 0.005 and accidents are independent of each other.(i) What is the probability that in any given period of 400 days there will be an accident on one day?(ii) What is the probability that there are at most three days with an accident?(iii) Find ?(2 < ? ≤ 4 /? < 3)
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The graph of the discrete probability to the right represents the number of live births by a mother 42 to 46 years old who had a live birth in 2015. Complete parts (a) through (d) below. 0.30 0-279 0.25 0.238 0,20- U.168 0.15 15 0.097 0.10 0.05 004 0036 0.043 0.00- 1 2 3 8 Number of Liive Births (a) What is the probability that a randomly selected 42- to 46-year-old mother who had a live birth in 2015 has had her fourth live birth in that year? 0.112 (Type an integer or a decimal.) (b) What is the probability that a randomly selected 42- to 46-year-old mother who had a live birth in 2015 has had her fourth or fifth live birth in that year? 0.206 (Type an integer or a decimal.) (c) What is the probability that a randomly selected 42- to 46-year-old mother who had a live birth in 2015 has had her sixth or more live birth in that year? 0.101 (Type an integer or a decimal.) hp esc & 8

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