A delivery truck travels from point A to point B and back using the same route each day. There are fourtraffic lights on the route. Let X denote the number of red lights the truck encounters going from A to B andY denote the number encountered on the return trip. Data collected over a long period suggest that theprobability distribution for (X, Y) is given byX/Y1340.010.010.030.070.0110.030.050.080.030.0220.030.110.150.010.030.010.0130.020.070.100.0140.010.060.030.01a. Is the random variables independent? support your answer.b. Find P(X > 1, Y > 2)c. Find the correlation of the two random variables and interpret the findings

a. P(x1 + x2 = 4 ) = P(0,4) + P(1,3) + P(2,2) + P(3,1) + P(4,0) = 0.01+0.03+0.15+0.07+0.01…

Answered: A delivery truck travels from point 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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A manufacturer has developed a new fishing line, which he claims has a mean breaking strength of 15 kilograms with a standard deviation of 0.5 kilogram. To test the hypothesis that μ=15μ=15 kilograms against the alternative that p<15p<15 kilograms, a random sample of 50 lines will be tested. The critical region is defined to be x<14.9x<14.9(a) Find the probability of committing a type 1 error when H0H0 is true(b) Evaluate ββ for the alternatives p−14.8p−14.8 and μ=μ= 14.9 kilograms.
A tax accountant would like to test the claim that the proportion of individuals who owe when filing their taxes is less than 0.20. If the z− test statistic was calculated as z=−2.11, does the tax accountant have enough evidence to reject the null hypothesis? Assume α=0.005. Move the blue dot to choose the appropriate test (left-, right, or two-tailed). Then, use the graph below to show the test statistic, p-value, and the rejection region to make a conclusion about the hypothesis test. powered by Move the blue dot to choose the appropriate test α=0.01 α=0.025 α=0.05 α=0.1 Significance level = 0.01 Select the correct answer below: There is enough evidence to suggest the proportion of individuals who owe when filing their taxes is less than 0.20. There is not enough evidence to suggest the proportion of individuals who owe when filing their taxes is less than 0.20. There is enough evidence to suggest the proportion of individuals who owe when filing their taxes is greater than 0.20.…
If the random variable X follows the uniform distribution U= (0,1) What is the distribution of the random variable Y= -2lnX. Show its limits.
Let X1, ..., Xn be a sample from a geometric random variable with parameter p.(a) Find the maximum likelihood estimator for p.(b) Is the estimator unbiased?(c) Is the estimator consistent?
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A researcher is using a two-tailed hypothesis test with α = 0.01 to evaluate the effect of a treatment. If theboundaries for the critical region are t = ± 2.845, then how many individuals are in the sample
If X has a Pareto distribution with parameters α and β and if c is a positiveconstant, show that Y = cX has a Pareto distribution with parameters α and β/c.
Assume I observe 3 data points x1, x2, and x3 drawn independently from anunknown distribution. Given a model M, I can calculate the likelihood for each data point as Pr(x1 | M) = 0.5, Pr(x2 | M) = 0.1, and Pr(x3 | M) = 0.2. What is thelikelihood of seeing all of these data points, given the model M: Pr(x1, x2, x3 | M)?
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A random sample of 100 freshman showed 6 had satisfed the university mathematics requirement and a second random sample of 50 sophomores showed that 13 had satisfied the university mathematics requirement. Enter answers below rounded to three decimal places. (a) The relative risk of having satisfied the university mathematics requirement for sophomores as compared to freshmen is (b) The increased risk of having satisfied the university mathematics requirement for sophomores as compared to freshmen is
A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percentage. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally, 65 seniors reported using drugs or alcohol within the past month, while 60 national seniors reported using them. Conduct a hypothesis test at the 5% level.NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) State the null hypothesis. H0: plocal ≠ pnational H0: plocal > pnational H0: plocal = pnational H0: plocal < pnational Part (b) State the alternative hypothesis. Ha: plocal < pnational Ha: plocal = pnational Ha: plocal ≠ pnational Ha: plocal > pnational…

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