Consider a model of random interest rates Ri between year i and i+1. The Ri are i.i.d. random variables such that 1+Ri is LogNormal(0.03,0.0010) distributed. Suppose you deposit an amount of £5000 at time 0. A) Determine the expectation value of Ri B) Determine the expectation value of the amount of money on your account after 10 years. C) Determine the probability that the money accumulated at time i=10 is more than £ 7500.

Consider a model of random interest rates Ri between year i and i+1. The Ri are i.i.d. random variables such that 1+Ri is LogNormal(0.03,0.0010) distributed. Suppose you deposit an amount of £5000 at time 0. A) Determine the expectation value of Ri B) Determine the expectation value of the amount of money on your account after 10 years. C) Determine the probability that the money accumulated at time i=10 is more than £ 7500.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

A microprocessor that controls the tuner in color TVs fails completely at random (that is, according to the exponential distribution). Suppose that the likelihood that a microprocessor that has survived for k years fails in year k + 1 is .0036. What is the cumulative distribution function of the time until failure of the microprocessor?
In game of roulette, a player can bet on the 1/38 probabilty of metal batt landa on 1the player gets to keep the paid to play the game and the player is awarded an additional 140 Otherwise, the player is awarded nothing and the casino takes the player's $4. Find the expected value E(x) to the player for one play of the game to player in a game of chance, then E(x) is negative. This value gives the average amount the player can expect to lose.
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?
2 The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second). (a) Find the probability that the demand will exceed 250 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.) (b) What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.02? (Round your answer to two decimal places.) cfs
If A, u are the rates of arrival and departure in an M/M/1 queue respectively, give the formula for the probability that there are n customers in the queue at any time in the steady-state.
9
Calculate each Poisson probability: (a) P(X=2), λ = 0.10 (Round your answer to 7 decimal places.) Probability
The life X (in hours) of a battery in constant use is a random variable with exponential density. What is the probability that the battery will last more than 12 hours (h) if the average life is 8 h?
local gym has only one treadmill machine for cardio exercises. Suppose exponential interarrival times with mean of 2 per hour, and exponential usage times with mean of 30 minutes per customer. Suppose a person has just arrived at 12.00 noon to use Assume your the machine. What is the probability that the next arrival will come before 1.00 pm, between and after 2.00 pm? Note that you have to provide three 1.00 pm and 2.00 pm, answers, one for each. Suppose no customer arrives before 1.00 pm. What is the probability that the next arrival will come between 1.00 pm and 2.00 pm? What is the probability that the number of arrivals between 1.00 pm and 2.00 pm will be zero (one, more than one)?