A fast-food restaurant operates both a drivethrough facility and a walk-in facility. On a randomly selected day, let X and Y, respectively, be the proportions of the time that th drive-through and walk-in facilities are in use, and suppose that the joint density function of these random variables is: f(r, y) = S(z+ 2y), 0
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- a) Let Y₁, Y2,..., Yn denote a random sample of size n taken from a distribution with probability density function given by : -y-μ 1 В f(y,μ,B)= 2B e 0 ,y>μ and p>0 elsewhere Assuming μ = 0, find an estimator, ß for the parameter ß using method of moment.2)Let X1, X2, ..., Xn be a sample of n units from a population with a probability density function f (x I θ)=θxθ-1 , 0<x<1, θ>0 . According to this: Find the maximum likelihood estimator (MLE) of parameter θ.let X and Y are two random variables with p.d.f as f(x,y)=3x2y+3yx2 0<x<1 0<x<1.find conditional density of X given Y?.Find mean mode and standard deviation of r.v Y?. Correlation between X and Y?. check that X and Y are independent or not?.
- 1. Let X1,..., X, be a random sample from a distribution with pdf f(x) = 2x, 0< x < 1. Compute the joint density of the smallest and the largest order statisics.The weekly sales for a drinking water product (in 1000s of liters) is a continuous random variable Y with probability density function (pdf)f(y) v-1) 0please teach this I do not no notationsLet Y1, Y2,..., Y, denote a random sample from the density function given by 1 yª-'e=y/®, y> 0, f(y[a, 0) = elsewhere, where a > 0 is known. a Find the MLE Ô of 0. b Find the expected value and variance of ê. c. Is the MLE ô an unbiased estimator for 0?Let Ap and B be the random variables. A random process is defined a X () = Ag cos ont+ B sin ant, where og is a real constant. Find the power density spectru m of X (), if Ag and B, are uncorrelated random variables with zero mean and same variance.The total number of hours, measured in units of 100 hours, that a family uses a vacuum cleaner in a period of one year is a continuous random variable X that has the following density function:X que tiene la siguiente función de densidad: 0Suppose X and Y are independent random variables. X iş uniformly distributed on (0,) and Y is exponentially distributed with 1=2. Find the joint density function f(x, y) of X and Y.Let Y₁, Y₂,..., Yn be a random sample from the inverse Gaussian distribution with probability density function: f(y, μ, 2) = { Where μ and are unknown. a) What are i. 1 -ACT √ λ 2ny3)že elsewhere if y > 0 the likelihood ii. the log likelihood functions of u and λ. b) Find the maximum likelihood estimators of u and 2.Recommended 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