onsider a random sample X₁.X₂X10 from a population distributed with the llowing density function: If Y = ²X₁, then 21-11 {zet, f(x)= B for x > 0 elsewhere State with parameter(s) the probability distribution of Y. What is the mean and variance of the statistic Y? Compute the probability that Y is at least 39.997. Find the value of t and p if P(t
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- Y has a distribution function (0, ys0, 24 F(y) = 0A Moving to the next question prevents changes to this answer. tion 9 Elongation (in %) of steel plates treated with aluminum is a random variable with the probability density function for 18 < x < 24 f(x) = {126 otherwise Find the variance of the elongation. O 2.980 O 8.222 5.297 O 3.190 A Moving to the next question prevents changes to this answer. MacBoo5.3-2 The random variable X has probability density function - {2(1-x). 0, 5.3-3 f(x) = 0 b probability histogram of the data. 2(1-x). 0≤x≤ 1, otherwise. Graph the probability density function of X. Find and graph the cumulative distribution function of X. Generate 1000 values for X and make an empirical probability histogram of the data. The random9. Zero-mean Gaussian random variables x and y have variance oz= 3 and o= 4 respectively and a y -1 correlation coefficient p = ing Write an expression for the joint density function.How many words can be formed by permutation of the letters of the word DEPRESSION such that each obtained word does not contain 2 consecutive identical letters? (Hint: use the principle of inclusion and exclusion)1.4 The pH of milk samples from Dairy Belle is a random variable Y with probability density function given by ((1/9)(4 – y)?,513 Let X be the standard normal distribution and consider the transformation given by Y = 1/X. Select all answers that apply. Select all answers that apply. Note exp(z) = e^z %D %3D Choose all that apply. O The density of Y is: g(y) = (1/2*pi)^(1/2) * (1/y^2)*exp(-1/(2y^2)) The density of Y is: g(y) = (1/2*pi)^(1/2) *exp(-1/(2y^2)) The values of y for which the density is non zero is y0. The values of y for which the density is non zero is y>0. %3D1. The density function for random variable X is f(x). Find variance for the random variable X. Leave your answers as reduced fractions. f(x) = {16 x+0Question 2. A continuous random variable, X has the following probability density function: S(x) = cx² 0sxs10 = 0 otherwise a) Find the value of c. b) Find the mean, median, mode, standard deviation and coefficient of variation. c) Find the probability that X is greater than 3.0 given that X is between 2.0 and 5.0.Probability and statsPlease help me with the following questionAnswer the following for the random variable X whose density function is f(x). f(x) = 840x^3(1-x)^6 0<x<1 0 elsewhere Find the mean and the variance. Mean: _________________ Variance: _________________ P(0.8 < X < 1) = ______________________SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON