Answered: kness of a chip (X) has a mean of 10…

kness of a chip (X) has a mean of 10 micrometers and chev's inequality, find a bound for the probability that 14 micrometers. t for some a and b, P(a < X < b) is at least 8/9. Find

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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Show that variance o? = (x²) – ((x))²
'Time headway' in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X be the time headway for two randomly chosen consecutive cars (in seconds). Suppose X has pdf f(x) = {* F(x) (a) Find the value of k. (b) Obtain the mean value of headway and the standard deviation of headway. (c) The cdf of X is = x > 1 x ≤ 1 0 1- x ≤ 1 x>1 Using the cdf, determine the following probabilities. (i) What is the probability that observed depth is at most 3? (ii) What is the probability that observed depth is between 3 and 2?
4. Consider the following joint pdf, where X is the amount of time (in hours) employees at a certain company spend commuting per day and Y is the percentage of each commute spent in a traffic delay. f(x) = }4 0 < x < 4, 0
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17. In Problem 11 from the previous section, westated that the damage amount is normally distributed. Suppose instead that the damage amount istriangularly distributed with parameters 500, 1500,and 7000. That is, the damage in an accident canbe as low as $500 or as high as $7000, the mostlikely value is $1500, and there is definite skewnessto the right. (It turns out, as you can verify in @RISK,that the mean of this distribution is $3000, thesame as in Problem 11.) Use @RISK to simulatethe amount you pay for damage. Run 5000 iterations. Then answer the following questions. Ineach case, explain how the indicated event wouldoccur.a. What is the probability that you pay a positiveamount but less than $750?b. What is the probability that you pay more than$600?c. What is the probability that you pay exactly $1000(the deductible)?
(5) If Xis a r.v. with mean u and variance o?, using Chebyshev's-Inequality, AX-2 20) S (a) 0.5 (b) 0.05 (c)0.657 (d) 0.25.
Please answer number2
If E(X) = 2 and standard deviation of X is 3, what is E(X2)?
3. The length of time required by students to complete a 1 hour exam is a random variable with a pdf given by: f (x) = = ca + for 0 sæ<1 a. Find c. Enter c as a reduced fraction. C = b. Find F(x). Enter coefficients as reduced fractions and use ^ to denote powers. F(x) = c. Find the probability that a student takes less than 30 minutes to complete the exam. Enter the probability as a reduced fraction. prob = d. Find the median length of time to take the exam. Enter your answer in hours with 4 decimal places. median = hours e. Find the length of time for the first 10% of the students to complete the exam. Enter your answer in hours with 4 decimal places. hours answer = f. Find the expected value, variance, and standard deviation of X. Enter your answer in hours with 4 decimal places (or hours squared in the case of variance), hours expected value =
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A company is studying the relationship between the mean annual percent return on capital (profitability) (y) and the mean annual percentage sales growth (x) for eight acrospace and defense companies. The data are summarised as follows: n=8, Σχ=1106, Σv=1399, Στ΄ = 2662.14, Στ’ = 2784.65, Σαν =1897.68 (a) (b) (d) Compute the product-moment correlation coefficient for the data. Interpret your result. Obtain the least square regression line equation. Calculate the coefficient of determination for the above data and comment on your answer. Find the value of profitability's percentage when the sales growth is 10 percent.