Let X, be i.i.d random sequence of a Normal random variables with mean zero and variance o?.X,+X_Define a new random sequence Y, = -2i. Determine mean of Y,ii. Determine auto-covariance of Y,iii. Determine cross-correlation between X, and Y,: E[X, Ym]iv.whether Y, is W.S.S or notDetermine the joint pdf of Y1 and Y2vi.V.For o =2, determine the probability P(0

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Answered: Let X, be i.i.d random sequence of a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The compressive strength of cement samples can be modeled by a normal distribution witha mean of (? + 6000) kilograms per square meter and a standard deviation of (? + 100)kilograms per square meter. Find the probability that a sample’s strength is between(? + 5800) kg/m2and (? + 5900) kg/m2 T = 28 ------------------------------------------------------------------------
Products A and B have the same daily demand distribution; Normal with mean 200 and standard deviation of 20. The correlation coefficient between their demands is -.7. If we pool the demands for A and B, the mean and standard deviation of (daily) pooled demand distribution would be, respectively, a) 282.8427 and 28.2843 b) 282.8427 and 15.4919 c) 400 and 15.4919 d) 400 and 28.2843
The lives (in hours of continuous use) of 100 randomly selected flashlight batteries are: Interval~ Frequency~ 6.95- 7.45 2 7.45- 7.95 8 7.95- 8.45 19 8.45- 8.95 39 8.95- 9.45 20 9.45- 9.95 10 9.95- 10.45 2 a.) Find the mean of the battery lives. ______ hours. b.) Find the standard deviation of the battery lives. ______ hours. (Type an integer or a decimal. Round to two decimal places.)
Suppose X~N(19, 2.5). Find the 50th percentile.
A researcher designs an experiment using two drugs, she prepares 15 independent flasks of yeast growth medium and yeast cells. She adds tunicamycin (T) or caffeine (C) to 5 flasks each. Remaining 5 flasks get no drugs (ND). Doubling time of the yeast cells are measured in each flask, data is in the table. Test if mean doubling time is different than others in at least one growth condition (ND, T or C), using F-test and report an approximate p-value for the level of significance. What is the hypotheses and the assumptions of this test?
Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 21 days and a standard deviation of seven days. (a) In words, define the random variable X. Edit Insert Formats BIUX₂ + 2+ 3 = C P & (b) Find the z-score for a trial lasting 19 days. your answer to three decimal places.) Shade: Left of a value (c) If one of the trials is randomly chosen, find the probability that it lasted at least 19 days. +||||||||| (d) Shade the area corresponding to this probability in the graph below. (Hint: The x- axis is the z-score. Use your z-score from part (b), rounded to one decimal place). -1 X² A ▾ A▾ -1.5 用 Σ+ Σ Α 2 Click and drag the arrows to adjust the values. (Round ++++++++++++ 3 4 (e) eighty-eight percent of all trials of this type are completed within how many days?
7. Let (z,.,) be a random sample from a normal distribution with mean ja and a variance at. Alo let S.. = , - z)* be the sum of squares of the randou sample. State without proof the sampling distribution of the following; (a) t(z) - ạ + b i-, 1,. n, as e positive eal constants. (- ) (b) t(z) - (E) (x) = (e) ti2) - (g) (r) = (e) t(2) = (d) t(a) Er, - E > ( - P (h) 시)- - -1 (-) (e) t(z)
how to find that which type of kurtosis is represent by the curve in sample distribution.
Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
Use this information about the overhead reach distances of adult females: µ = 205.5 cm, σ = 8.6 cm, and overhead reach distances are normally distributed (based on data from th Federal Aviation Administration) If 40 adult females are randomly selected, find the probability that they have a mean overhead reach between 204.0 cm and 206.0 cm.
Suppose X ~ N(3, 1.2). What value of x is two standard deviations to the right of the mean?
A technician suspect that the number of computer errors recorded per day in the LAN follows a Poisson distribution with a mean of 2 errors per day. Record of the number of errors per day for the past 260 days are shown in table below. Number of Number of Pr(X = x) E (0; – e;) Errors per days ei day 77 1 90 2 55 3 30 4 or more a. Test the hypothesis that the number of computer errors per day has the Poisson distribution with mean 2 at the 5% significance level. b. Find an approximate value of the p – value for the test statistics in (a). 8

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