Question 9 The number of years a radio functions is exponentially distributed with parameter1 = 1/8. If Jones buys a used radio, what is the probability that it will be working after anadditional 10 years?

Answered: Question 9 The number of years a radio…

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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QUESTION 1 Assume that sales for year “n" were 12 units and a forecast of sales for that year had been 10 units and you want to make a simple exponential smoothing forecast of sales for period “n+1." If alpha equals 0.6 the forecast for year "n+1" would be 11 11.2 10.8 11.5 12.2
Question no. 10 A machine is made up of two components that operate independently. The lifetime T; (in days) of component i has an exponential distribution with parameter Ai, for i = 1,2. Suppose that the two components are placed in parallel and that A1 A2 = In 2. When the machine breaks down, the two components are replaced by new ones at the beginning of the following day. Let Xn be the number of components that operate at the end of n days. Then the stochastic pro- cess {Xn,n probability matrix. 0,1,...} is a Markov chain. Calculate its one-step transition
Question 10: a) Suppose you have a log utility function. Suppose your current wealth W = $300,000. How much would you pay today (A) to insure yourself against a 10% probability of a $150,000 loss? b) Suppose you have a log utility function. Suppose your current wealth W = $300,000. How much would you pay today (A) to avoid a "fair gamble" with a 50% and 50% payoff of +$1000 or -$1000?
Many phenomena – from stock market prices to census data to heat capacitiesof chemicals – obey Benford’s Law. This law states that for a set of numericaldata, the proportion of numbers starting with the digit ? is approximately log10 (1 +1/D) Show that Benford’s Law predicts that around 30% of numbers will startwith a 1, and around 18% will start with a 2. What proportion of numbers does the law predict will start with a 9? Without using your calculators, show that 9∑ log10 (1 + 1/D)=1D=1
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Question 9 The number of years a radio functions is exponentially distributed with parameter a = 1/8. If Jones buys a used radio, what is the probability that it will be working after an additional 10 years?