Question 5X is a random variable and the probability density function of x isf (x) = 15 ³ for 0

Answered: Image /qna-images/answer/e14c0d6e-706f-4b91-9ba1-3a73479b3051.jpg

Answered: f(x) = 5x³ for 0

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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A population with u = 45 and o = 10 is standardized to create a new distribution withu= 100 and o = 20. In this transformation, a score of X = 15 from the original distribution will be transformed into a score of X =.
q2 a
Let X₁, ..., X be a random sample from a gamma distribution with a x = 2 and 3 = = 0. '1' 1. Find the simplified likelihood of 0 given x: L(01x). 2. Find the maximum likelihood estimator of 0,0 MLE* is unbiased. 3. Show that the value you found for 0 MLE
Let X. X , be a random sample of siren from a normal distribution with population mean 0 and population variance a>Ois unknown, that is N(0, ). Suppose that we define the following plvotal quantity (n-1)s where & and S' are the sample mean and the sample variance, respectively. Use the plvotal quantity (Q) to derive the (1- a) 100% confidence interval (C) for the unknown parameter (o) if the two critical values are q--n, a) and (n-1) (A) CI = (n8+(n-1)51 + n-1) s (8) CI - (C) CI - + (n-1) s (D) CI= O D O A O c O B
N= 150 observations were collected on a time series that was identified as a AR(2) time series. The following statistics were computed from the data. Mean - 45.0 Variance 15.6 Autocorrelation function (up to lag 5) r1 = 0.80, r2 = .50, rз = .26, r4 = -.10, rs = 0.08: == Estimate the parameters of the model using the method of moments.
An experiment is conducted to compare the maximum load capacity in tons (the maximum weight that can be tolerated without breaking) for two alloys A and B It is Kknown that the two standard deviations in load capacity are equal at 7 tons each. The experiment is conducted on 50 specimens of each alloy (A and B) and the results are X = 75.8. X = 71.8, and X-X=4. The manufacturers of alloy A are convinced that this evidence shows conclusively that Hug and strongly supports the claim that their alloy is superior. Manufacturers of alloy 8 claim that the experiment could easily have given X-X 4 even if the two population means are equal. Complete parts (a) and (b) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) Make an argument that manufacturers of alloy B are wrong. Do it by computing P(XA-XB41 PA-HB) P(XA-X > 4) - @
To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 43 feet. Assume the population standard deviation is 4.6 feet. The mean braking distance for Make B is 46 feet. Assume the population standard deviation is 4.5 feet. At α=0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles? Assume the samples are random and independent, and the populations are normally distributed. The critical value(s) is/are Find the standardized test statistic z for μ1−μ2.
A random sample of 10 observations from population A has sample mean of 152.3 and a sample standard deviation of 1.83. Another random sample of 8 observations from population B has a sample standard deviation of 1.94. Assuming equal variances in those two populations, a 99% confidence interval for μA − μB is (-0.19, 4.99), where μA is the mean in population A and μB is the mean in population B. (a) What is the sample mean of the observations from population B? (b) If we test H0 : μA ≤ μB against Ha : μA > μB, using α = 0.02, what is your conclusion?
For 50 randomly selected speed dates, attractiveness ratings by males of their female date partnerS (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield *= 6.3, y = 6.1. r= - 0.283, P.value = 0.046, and g = 8.39 - 0.369x. Find the best predicted value of y (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x= 4. Use a 0.01 significance level. see score The best predicted value of g when x= 4 is 7. (Round to one decimal place as needed.)
The desired percentage of SiO₂ in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO₂ in a sample is normally distributed with = 0.32 and that x = 5.23. (Use a = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5? State the appropriate null and alternative hypotheses. O Ho: μ = 5.5 H₂:μ> 5.5 O Ho: μ = 5.5 H₂: μ = 5.5 ⒸHO: μ = 5.5 H₂:μ ≥ 5.5 O Ho: μ = 5.5 H₂: μ< 5.5 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) Z = P-value = State the conclusion in the problem context. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true verage percentage differs from the desired percentage. O Reject the null hypothesis. There is not sufficient evidence to…
4
For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield *= 6.4. y = 6.0, r= - 0.279, P-value = 0.050, and g = 8.27 - 0.357x. Find the best predicted value of y (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x=7. Use a 0.10 significance level. The best predicted value of y when x = 7 is (Round to one decimal place as needed.)

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