2) Consider the random variable Y has a normal distribution with the following probability density function1-y?+44y–48418f(y)3/270 < y <a) What is the mean and variance of Y?b) What is the median of Y?

Given Y follow normal distribution and its probability density function is shown below…

Answered: 2) Consider the random variable Y has 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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Let Y, represent the ith normal population with unknown mean #, and unknown variance of for i=1,2. Consider independent random samples, Ya, Ya, Yin, of size n,, from the ith population with sample mean Y, and sample variance S² = (₁-P) ². (d) Define V₁, a function of S1, that has a chi-square distribution. (e) Is V₁ a pivotal function to find a confidence interval for o?? Explain with argument. (f) Find a (1-a) x 100% confidence interval for of
This is a Statistics problem. Are the random variables Z1+Z2 and Z1-Z2 the same? Do they have the same distribution?
If the random variable X as a mean of u and a variance of o2 what is the P((X-u)² < 20): O less that equal to 1/4 O greater than or equal to 3/4 cannot tell O equal to 5/4
If a discrete random variable X has the following probability distribution: X -2, - 1, 0, 1, 2 P(X) 0.2, 0.3, 0.15, 0.2, 0.15 Use this to find the following: (a) The mean of X and E[X^2]. (b) The probability distribution for Y = 2X^2 + 2 (i.e, all values of Y and P(Y )). (c) Using part (b) (i.e, the probability distribution forY ), find E[Y ]. (d) Using part (a), verify your answer in part (c) for E[Y ]. **Note: Please do not just copy from Chegg!
5. Let (Xi, Yi), i 1, 2, ,n, be a random sample from a bivariate normal distribution. Find the joint distribution of (X,Y).
Suppose random variable Y represents a random number generator that can take any value between 1 and 11. Then the density curve of the outcomes has constant height between 1 and 11, and height of 0 elsewhere. What’s the height of the density curve between 1 and 11? What is the probability that Y<2? What is the probability that Y=2? Can Y=2 happen as an event for this random number generator? What is the probability that Y=0? Can Y=0 happen as an event for this random number generator?
Please help with this practice problem
3. The level of impurity (in percent) in the product of a certain chemical process is a random variable with probability density function 3 64 -x²(4 - x) 0 0 < x < 4 otherwise a. What is the probability that the impurity level is greater than 3%? b. What is the probability that the impurity level is between 2% and 3%? c. Find the mean impurity level. d. Find the variance of the impurity levels.
In its Fuel Economy Guide for 2008 model vehicles, the Environmental Protection Agency gives data on 1152 vehicles. There are a number of outliers, mainly vehicles with very poor gas mileage. If we ignore the outliers, however, the combined city and highway gas mileage of the other 1120 or so vehicles approximately Normal with mean 18.7 miles per gallon (mpg) and standard deviation 4.3 mpg. Question: The quintiles of any distribution are the values with cumulative proportions 0.20, 0.40, 0.60, and 0.80. What are the quintiles of the distribution of gas mileage?
1.Which of the following statements about a standard normal variable is true? a) It has a standard deviation of zero b) The total area under the standard normal curve is sometimes approximately equal to one c) It has a mean of zero and standard deviation of one d) Most of the time, the area under the half of the standard normal curve is approximately equal to one-half 2. Which of the following does not apply to the normal distribution? a) The normal curve is unimodal (that is, it has one mode) b) The total area under the curve is equal to one c) The normal curve is symmetric about its standard deviation d) The mean and the median are equal

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2) Consider the random variable Y has a normal distribution with the following probability density function 1 -y²+44y-484 18 f(y) 3/27 0 < Y a) What is the mean and variance of Y? ɔ) What is the median of Y?