Let i, denote the effective annual return achieved on an equity fundachieved between time (t-1) and time t.Annual log-returns on the fund, denoted by In(1+i), are assumed to forma series of independent and identically distributed Normal randomvariables with parameters u = 6% and σ = 14%.An investor has a liability of £10,000 payable at time 15.Calculate the amount of money that should be invested now so that theprobability that the investor will be unable to meet the liability as it fallsdue is only 5%.

Given that an investor has a liability of £10,000 payable at time 15.

Answered: Let i, denote the effective annual…

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...

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Exercise 3. Let X be a random variable with mean and variance o². For a € R, consider the expectation E((X-a)²). a) Write E((X-a)²) in terms of a, u and o². b) For which value a is E((X - a)²) minimal? c) For the value a from part (b), what is E((X-a)²)?
In a simulation study on cyber attacks, the researcher is interested to investigate on whether the attack(s) are successfully performed. Let A define the event that an attacker has successfully performed the attack. If Pr(A) = 0.13, what is the probability Pr(A')?
The annual rainfall (in inches) in a certain region is normally distributed with µ = 40 and σ = 4. What is the probability that starting with this year, it will take more than 10 years before a year occurs having a rainfall of more than 50 inches? Suppose the rainfall in each year is independent of the rainfall in other years and the distribution of rainfall in each year is the same as in the present year.
Assume the lifetime of electronic systems T (based on months) has Exponential distribution with λ=0.01. We select a random sample of 5 systems (random lifetime of these systems are T1, T2, T3, T4, and T5). Assume, S= T1+T2+ T3+ T4+ T5. a. Find E[S] . b. Find Standard Deviation of S (σSσS). c. Find median of T1.
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.
Consider the distribution of Binomial, Poisson, Exponential, Gamma, and let T1=X+4 and T2=(X-1) Check the property of biasdness
A technician discovered that the cumulative distribution function (CDF) of the lifespan of bulb in years is given by f(y) = -10 ye 10 100 0
In the transmission of digital information, the probability that a bit has high, moderate, and low distortion is 0.01, 0.04, and 0.95, respectively. Suppose that three bits are transmitted and that the amount of distortion of each bit is assumed to be independent. Let X and Y denote the number of bits with high and moderate distortion out of the three, respectively. Determine: (c) E(X)= i Round your answer to two decimal places (e.g. 98.76).
İf X follows the Poisson probability law such that P (xr 1) = P (x = 2). then ind the probability of 4 successes.
The time that it takes to service a car is an exponential random variable with rate 1.1. If A brings his car in at time 0 and B brings his car in at time t, what is the probability thatB’s car is ready before A’s? Assume that the service times are independent, and the servicebegins upon arrival.2. If both cars are brought in at time 0, with work starting on B’s car only when A’s car has beencompletely serviced, what is the probability that B’s car is ready before 2? Detailed explanation and calculation would be much appreciated.
You are planning to go fishing with two friends. The time (in hours) before you catch a fish is exponentially distributed with parameter 6. How long do you need to arrange for the fishing so that there is a 95% probability that everyone catches at least one fish? [Assume that the events that each person catches a fish are independent.]
Let A and B be independent exponential random variables, both with mean 1. If U = A + B and V = A/B, find the joint pdf of U and V.

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