3) A uniformly distributed continuous random variable, X, is described by the PDF shown. It is input into asystem producing a new random variable Y, described by the equation shown. Determine an expressionfor the CDF for Y as a function of fx(x). You do not need to solve non-trivial integrals. Just set them up.-2fx(x)1/42 xy= g(x)= |x|

We have a uniformly distributed continuous random variable X with the probability density function…

Answered: 3) A uniformly distributed continuous…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 9T

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Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
f(X)= 3/8( 4x - 2x2 ) 0<* x <* 2 (* less or equal to) a. Find the variance of X.
Pv. Don't provide handwriting solution
If E(X) = 6 and E[(X)(X-1)] = 51, a) find the second moment b) find the variance of X Please provide your working and round your answers to 3 decimal places
Prove that the variance of b, V(b) = o²(X'X)−¹
Please answer all part : Let rt be a log return. Suppose that r0, r1, . . . are i.i.d. N(0, 0.01^2). (a) What is the distribution of rt(8) = rt + rt−1 + rt−2 +...+ rt−7? (b) What is the covariance between r7(3) and r9(3)? (c) What is the conditional distribution r17(3) given that r16 =0.004 (d) What is the probability that the gross return over the first 10 times periods is at least 1.05?
"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 = the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow. The pdf of X is the following. 0.17e-0.17(x - 0.5) - {0.17e-0.1 x ≥ 0.5 otherwise (a) What is the probability that time headway is at most 6 sec? (Round your answer to three decimal places.) f(x) = (b) What is the probability that time headway is more than 6 sec? At least 6 sec? (Round your answers to three decimal places.) more than 6 sec at least 6 sec (c) What is the probability that time headway is between 5 and 6 sec? (Round your answer to three decimal places.)
Use the data in vapor.csv, obtain the transformed predictor 1/X, and the transformed response log(Y), where "log" refers to the natural logarithm. Denote the new predictor by X*(=1/X) and denote the new response by Y*(=log Y). Fit a least squares model for the new response and the new predictor. It turns out that the estimated intercept is [ PUT ANSWER HERE ] , and the estimated slope is[ PUT ANSWER HERE ] . The estimated standard error of the estimated slope is [ PUT ANSWER HERE ] , and the value of the F statistic associated with this fitted model is equal to [ PUT ANSWER HERE ]. Note: The data in vapor.csv is attached as an image
a) Let X1,..., Xn be iid with pdf f(x;0) the method of moments estimator of 0, and calculate its mean and variance. Is the method 1/0 for 0 0. Find of moments estimator unbiased for 0? Let X1,..., Xn be iid with pdf f(x;0) = 0xº-1 for 0 0. Find the method of moments estimator of 0. b) c) Let X1,..., Xn be iid with pmf P(X = x) = 0"(1 – 0)1-¤ for x = 0 or 1, and 0 < 0 < 1/2. Find the method of moments estimator of 0, and calculate its mean squared error.
Show all work. If a calculator function is used, write out the input commands, (i.e. invNorm(0.01,0,1)). SRS of 42 students are polled and asked if their average speed exceeded the speed limit on 19th avenue. From the sample, 30 admit to exceeding the speed limit. Using alpha α=0.05 , test the claim that the proportion of students who admitted to exceeding the speed limit is less than 75%. In space provided answer the following. (a)Write the null and alternative hypothesis. (b)State the test statistic. (c)Show the work or state the calculator inputs to find the p-value. (d)State the conclusion in words. Do not use symbols.
4. Suppose that X has pdf f(x) = 3x² for 0 < x< 1. Find the pdf of the random variable Y = VX.
Please write it in detail.

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