An investment firm offers its customers municipal bonds that mature after varying numbers of years.Given that the cumulative distribution function of T, the number of years to maturity for a randomly selected bond, is: a. Find P(1.4 3); Continuation is on the picture

An investment firm offers its customers municipal bonds that mature after varying numbers of years.Given that the cumulative distribution function of T, the number of years to maturity for a randomly selected bond, is: a. Find P(1.4 3); Continuation is on the picture

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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Changes in the earth's rotation are exceedingly small. However, a very long-term trend could be important. (Reference: Journal of Astronomy, Vol. 57, pp. 125-146.) Let I represent an increase and D a decrease in the rate of the earth's rotation. The following sequence represents historical increases and decreases measured every consecutive fifth year. D D D D D D I I D D D D D I I I I I I I I I I D I I I I I Test the sequence for randomness. Use ? = 0.05. (a) What is the level of significance? (b) Find the sample test statistic R, the number of runs. (c) Find the upper and lower critical values in the Critical Values for Number of Runs R table.
Hudson Marine provides boats sales, service, and maintenance. Boat trailers are one of its top sales items. Suppose the quarterly sales values for the seven years of historical data are as follows. Do not round intermediate calculations. a. Compute the centered moving average values (first find Four-Quarter Moving Average) for this time series (to 3 decimals). Centered Moving Average t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 Sales 5 17 8 6 9 16 16 7 14 24 22 12 18 26 26 20 24 33 28 23 22 36 29 18 28 42 33 28 9.625 Year 1 2 3 4 5 6 7 Quarter 1 5 9 14 18 24 22 28 Quarter 2 17 16 24 26 33 36 42 Quarter 3 B 16 22 26 28 29 33 Quarter 4 6 7 12 20 23 18 28 Total Yearly Sales 36 48 72 90 108 105 131
Stocks A and B have the following historical returns: Year 2016 2017 2018 2019 2020 a. Calculate the average rate of return for each stock during the period 2016 through 2020. Round your answers to two decimal places. Stock A: % % Stock A's Returns, ra (20.60%) 39.75 17.25 (3.50) 25.00 Stock B: b. Assume that someone held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would the realized rate of return on the portfolio have been each year? Round your answers to two decimal places. Negative values should be indicated by a minus sign. CV Stock A Stock B's Returns, B (14.30%) 29.80 37.30 (6.60) 11.70 Year 2016 2017 2018 2019 2020 What would the average return on the portfolio have been during this period? Round your answer to two decimal places. Portfolio % c. Calculate the standard deviation of returns for each stock and for the portfolio. Round your answers to two decimal places. Stock B % Portfolio % Stock A % Standard Deviation d. Calculate the coefficient of…
The following table shows a company's annual revenue (in billions of dollars) for 2009 to 2014. Year Period (t) Revenue ($ billions) 2009 23.8 2010 2 29.3 2011 3 38.0 2012 4 50.2 2013 59.8 2014 66.8 (a) Construct a time series plot. 80 T 80- 80- 80 T 70 70 70 70 60 60 60- 60 50 50- 50 0- 50- 40 40- 40 40 30 30 30 30 20 20 20 20 10 10 10 10- 0- 0- 1 3 4 5 6. 7. 1 2 3 4 5 6 7 0 1 2 3 4 6. 7 0 1 3 4 7 Period Period Period Perjod What type of pattern exists in the data? The time series plot shows a downward curvilinear trend. O The time series plot shows a downward linear trend. O The time series plot shows an upward curvilinear trend. O The time series plot shows an upward linear trend. (b) Develop a linear trend equation for this time series to forecast revenue (in billions of dollars). (Round your numerical values to three decimal places.) T: = (c) What is the average revenue increase per year (in billions of dollars) that this company has been realizing? (Round your answer to three…
For a wide sense stationary process: Select one: O a. the covariance is constant O b. all of these O c. the expected value is constant
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(Note : I want clear explanation of this numerical. Please solve within 45 minutes.) Studies of a machine component showed that the time the component operates before breaking down is exponentially distributed with a mean of 1000 hours. Calculate the maximum operating hours if the reliability is to be above 99% Options : a) 12.67 hours b) 9.54 hours c) 10.05 hours d) 6.58 hours
A graphing calculator is recommended. Straight-line depreciation is a method for estimating the value of an asset (such as a piece of machinery) as it loses value ("depreciates") through use. Given the original price of an asset, its useful lifetime, and its scrap value (its value at the end of its useful lifetime), the value of the asset after t years is given by the formula for 0 ≤ t ≤ (Useful lifetime). (a) A farmer buys a harvester for $40,000 and estimates its useful life to be 20 years, after which its scrap value will be $4000. Use the formula above to find a formula for the value V of the harvester after t years, for 0 ≤ t ≤ 20. (Do not use commas in your answer.) V = Value = Price - (b) Use your formula to find the value of the harvester after 5 years. V(5) = No Solution (c) Graph the function found in part (a) on a graphing calculator on the window [0, 20] by [0, 40,000]. (Hint: Use x instead of t.) Help 40000 30000 Price (Scrap value) (Useful Lifetime) 20000 10000 10 Fill…
The following time-series diagram tracks the performance of two stocks during the month of October. Describe the overall trend of the two stocks. By what percentage did the value of each stock increase or decrease during the month of October? Stock 2 $200 Stock 1 T$150 Stock 2 -$100 Stock 1 T$ 50 1 5 11 16 21 26 31 October a. Stock 2 increased by 200%. Stock 1 decreased by 50%. b. Stock 2 increased by 100%. Stock 1 decreased by 50% c. Stock 2 increased by 200%. Stock 1 decreased by 33% d. Stock 2 increased by 100%. Stock 1 decreased by 33%.