An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is the following.12 3p(y)0.550.250.150.05(a) Compute E(Y).E(Y) = (No Response)(b) Suppose an individual with Y violations incurs a surcharge of $120Y. Calculate the expected amount of the surcharge.$ (No Response)

Answered: Image /qna-images/answer/d17f0d1f-ac53-4dc8-8c5d-17018672db9b.jpg

Answered: An individual who has automobile…

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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In an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from y = 0.98x2.1for one year to y = 0.32x2 + 0.68x for the next year. Find the Gini coefficient of income for both years. (Round your answers to three decimal places.) after before
The analysis of tooth shrinkage by C. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is con-tinuing to decrease and that the evolutionary process has not yet come to a halt. In northern Europeans, for example, tooth size reduction now has a rate of 1% per 1000 years. a. If t represents time in years and y represents tooth size, use the condition that y = 0.99y0 when t = 1000 to find the value of k in the equation y = y0 ekt. Then use this value of k to answer the following questions. b. In about how many years will human teeth be 90% of their present size? c. What will be our descendants’ tooth size 20,000 years from now (as a percentage of our present tooth size)?
Determine the upper-tail critical value tα/2 in each of the following circumstances.
The analysis of tooth shrinkage byC. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is continuing to decrease and that the evolutionary process has not yetcome to a halt. In northern Europeans, for example, tooth sizereduction now has a rate of 1% per 1000 years.a. If t represents time in years and y represents tooth size, usethe condition that y = 0.99y0 when t = 1000 to find thevalue of k in the equation y = y0ekt. Then use this value of kto answer the following questions.b. In about how many years will human teeth be 90% of theirpresent size?c. What will be our descendants’ tooth size 20,000 years fromnow (as a percentage of our present tooth size)?
In the production of synthetic motor lubricant from coal, a new catalyst has been discovered that seems to affect the viscosity index of the lubricant. In an experiment consisting of 23 production runs, 11 used the new catalyst and 12 did not. After each production run, the viscosity index of the lubricant was determined to be as follows. With catalyst 4.0 4.4 2.6 1.2 3.9 4.2 2.8 3.2 4.1 2.1 1.6 Without catalyst 3.3 2.3 3.7 3.0 4.3 2.7 4.5 1.5 3.6 2.5 2.2 3.4 The two samples are independent. Use a 0.01 level of significance to test the null hypothesis that the viscosity index is unchanged by the catalyst against the alternate hypothesis that the viscosity index has changed. 1.) Find the sample test statistic. (Use 2 decimal places.)2.) For the sign test, rank-sum test, and Spearman correlation coefficient test, find the P-value of the sample test statistic. For the runs test of randomness, find the critical values from Table 10 of Appendix II. (Use 4 decimal places.)
If X1, X2, ... , Xn constitute a random sample of size n from an exponential population, show that X is a consis-tent estimator of the parameter θ.
If X is exponentially distributed with parameter λ and Y is uniformly distributed on the interval [a, b], what is the moment generating function of X + 2Y ?
An efficiency study of the morning shift at a factory (7:00 A.M. to 12:00 noon) indicates that an average worker who arrives on the job at 7:00 A.M. will have produced Qunits t hours later, whereQ(t) = -t3 + 9t2 + 15tWhen during the morning shift does the worker’s production reach the point of diminishing returns?
A certain brand of upright freezer is available in three different rated capacities: 16ft3, 18 ft3, and 20 ft3. Let X = the rated capacity of a freezer of this brand sold at acertain store. Suppose that X has pmfx 16 18 20p(x) .2 .5 3a. Compute E(X), E(X2), and V(X).b. If the price of a freezer having capacity X is 70X – 650, what is the expectedprice paid by the next customer to buy a freezer?c. What is the variance of the price paid by the next customer?d. Suppose that although the rated capacity of a freezer is X, the actual capacityis h(X) = X - .008X2. What is the expected actual capacity of the freezer purchasedby the next custom
Consider the following initial-value problem.
Suppose that the Lorenz Curve for country A is given by yA = x 2.2 and for country B is yB = 0.3x 2 + 0.7x. Use the Gini index to determine which of the two countries has greater inequality in its income distribution.
Apply Taylor’s method of order two with N = 4 to the initial-valueproblem

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