Find the conditional variance of X, given Y, where X and Y are random variables svith the joint density XY (x, y) =1 for 0 0 sxrs1, 0
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Q: i) Derive the standard error of ß, se(B) = 0.0009, using MLE approach. ii) Find an approximate 95%…
A: Firstly it is required to determine the MLE of the parameter and then the variance to get the…
Q: Let the joint pdf for the continuous random variables X and Y be: f(x,y) = { 4xy; 0<x<1, 0<y<1…
A: Let the joint pdf for the continuous random variables X and Y be:f(x,y) = {4 xy; 0<x<1,…
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- The joint probability function of two discrete random variables X and Y is given by f(x,y)=(1/42) (2x+y) where, x=0,1,2; y=0,1,2,3. Find P(x21, ys2). Use 4 decimal places.Consider the continuous random variable with probability density function fx(x) = 3x² for 0Do last two partThe number of minutes that train is early or late can be modeled by a random variable whose density is given by: g(t) = {(1/972)(81 − t^2), −9 ≤ t ≤ 9, 0 elsewhere, where negative values indicate the train arriving early and positive values indicate the train arriving late. a. Find the probability that one of the train trips will arrive more than 5 minutes early. b. Find the probability that one of the train trips will arrive between 1 and 8 minutes late. c. Without integration, give the expected number of minutes early/late. Examination of the graph and recollection of properties of integrals will allow this.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: 0plz dont copy the answers from others, rly need it to studySuppose that the amount of time a hospital patient must wait for a nurse's help is described by a continuous random variable with density function f(t) = e-t/3 where t≥ 0 is measured in minutes. (a) What is the probability that a patient must wait for more than 4 minutes? (b) A patient spends a week in the hospital and requests nurse assistance once each day. What is the probability that the nurse will take longer than 5 minutes to respond on (exactly) two occasions? (c) What is the probability that on at least one call out of seven, the nurse will take longer than 7 minutes to respond?For a laboratory assignment, if the equipment is working, the density function of the observed outcome X is f(x) = 2x(1-x), 0 < x < 1 Find the variance and standard deviation of Xc) Let Y₁, Y₂,..., Yn be a random sample whose probability density function is given by f(v:B)= 684 - fa 00 0, elsewhere 200 200 200 and suppose that n = 200, y = 20, y = 100, y = 250 and $ = 0.025. i=1 i) Derive the standard error of ß, se(B) = 0.0009, using MLE approach. ii) Find an approximate 95% Confidence interval for B.AsapLet x be a random variable with a density function I (2) = { "0, 6x (1 – a), 0 < x < 1 elsewhere By finding the fırst and second moments, calculate the variance of x [1] (answer correct to 1 dp)Let Z₁ = X₁-μx ~N(0,1), and Wi σχ = Yi-HY~N(0,1), for i = 1,2,3,...,10, then: oy i) State, with parameter(s), the probability distribution of the statistic, T = ii) Find the mean and variance of the statistic T = Σt, wi? Σ, Z² Σt=1Zi 4i=1 iii) Calculate the probability that a statistic T = Z₁ + W₁ is at most 4. iv) Find the value of such that P(T > B) = 0.01, where T = Σ₁₁Z₁² + 10₁ W₁². ẞ Σ{1Z2 Σi,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