The length of time, in minutes, for an airplane to obtain clearance for takeoff at a certain airport is a random variable Y = 5X -2, where X has the following density function. Find the mean and variance of the random variable Y.1x>0f(x) = { 7e0,The mean of Y is(Type an integer or a fraction.)The variance of Y is(Type an integer or a fraction.)

Answered: Image /qna-images/answer/87fd0663-b22b-4867-af11-eb00041d0ea0.jpg

Answered: The length of time, in minutes, for an…

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 built-in data set, rock, is a data frame recording the measurements of rock sample from a petroleum reservoir. We are interested in the area column of rock. Using R we can convert this column into the vector x by the assignment x<-rock$shape. Assume that the n area measurements x=(x1, x2,...,xn) are a random sample from a population with true unknown mean ? and true unknown variance ?2. Remember, let x be defined by x<-rock$shape.
For a random variable X E(X) = 1.27, E(X²) = 3.79 The variance of X is equal to Select one: O 2.52 O 2.9843 O 2.1771 O 0.758 0.3351
Given pdf f (x) = 1.5x2 for −1< x < 1. Determine variance of X.
Let X-1: correct, X=0 : wrong And P= Pr(X=1)=2/5 What is the variance? .32 O.6 O .4
Let X be a normal random variable with mean 85 and a variance of 25 (i.e., X ∼ N (85, 25)). step1: Let M = aX + b for some constants a, b not equal to 0. Write an expression for the pdf of M . step 2: Suppose that X represents an approximate distribution of the final scores in a certain math course (ignore the fact that this approximation can technically have scores that are greater than 100 or less than 0). If the teacher were to curve the scores, it means he would determine a function to apply to the scores to achieve a desired distribution (assume an affine function in this case, as in the previous part). Suppose he wants the scores to be normally distributed with mean 80 and a standard deviation of 4. What should he choose for a and b? What students would see their score lowered, and what students would see their score increased?
Let G and H be two independent unbiased estimators of 0. Assume that the variance of G is two times the variance of H. Find the constants a andb so that aG + bH is an unbiased estimator with the smallest possible variance for such a linear combination.
Psi is a measure of compressive strength, or the ability of the material to carry loads and handle compression. The desired concrete psi rating used for sidewalks and residential driveways ranges from 2500psi to 3000psi obtained from mixing cement, stone, and sand in different ratios but with the same amount of water. The summary of the psi's of three (3) such concrete mixes made by three (3) different civil engineering students is given as follows: Mean vector: The variance-covariance matrix: Concrete mix Mean Concrete mix 1 Concrete mix 2 Concrete mix 3 Concrete mix 1 | Concrete mix 2 2700 18 12 2 3000 12 16 3 2400 Concrete mix 3 16 25 Let the random variable Y be the vector of the psi's of concrete mixes obtained by the students, i.e. Y1, denotes the psi of concrete mix made by student 1, Y2 is the psi of concrete mix made by student 2 and Y3 is the psi of concrete mix psi made by student 3. (a) Find (i) the multivariate probability distribution function (pdf) of Y. (ii) the…
Let L be the random variable for the length of time, in years, that a person will remember an actuarial statistic. For a certain popula- tion, L is exponentially distributed with mean 1/Y, where Y has a gamma distribution with a = 4.5 and 3 = 4. Find the variance of L.
Q1.2 Mean of X A medical practice collects data on its patients with respect to several personal habits. The following table gives the distribution of the number of alcoholic drinks consumed per day in that population of patients. X = # of drinks per day Probability Save Answer Q1.3 Variance of X X = # of drinks per day Probability 0 0.38 Find the mean for this random variable, that is find ux. Show your work in the space below. Save Answer A medical practice collects data on its patients with respect to several personal habits. The following table gives the distribution of the number of alcoholic drinks consumed per day in that population of patients. 0 0.38 Q1.4 Standard Deviation of X X = # of drinks per day Probability 1 0.32 0 0.38 1 0.32 2 0.25 Find the variance for this random variable, that is find (ox)². Only show the first and last term of the work required. 1 2 0.25 A medical practice collects data on its patients with respect to several personal habits. The following table…

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