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- please and thank you!!!b) Let X₁, X₂,..., X, denote a random sample of size n from a distribution with probability density function: i) ii) iii) f(x; 0) = {0(1-x)(¹+0), Find the maximum likelihood estimator of 0. Derive fisher's information of 0. suppose that 5 independent observations were taken from such a distribution: 4 1 3 5 4 and 0 = 0.7052 Find a 99% confidence interval for 0. x>0 elsewhere DAnswer with Solution.
- 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.Let X₁, X₂, X3,...,Xn be a random sample of n from population X distributed with the fol probability density function: 1 ze=20, f(x;0)=√√2n0 0, if -∞0b) Let X₁, X2, X3,...,Xn be a random sample of n from population X distributed with the following probability density function: f(x;0)=√√2n0 0, -20₁ if -∞0 < x <∞0 otherwise (i) Find the parameter space of 0. (ii) Find the maximum likelihood estimator of 0. (iii) Check whether or not the estimator obtained in (ii) is unbiased. (iv) Find the Fisher information in this sample of size n about the parameter 0.The probability density function for the continuous random variable X is given by: (А(х? — 2х + 21) 0Let X be a point randomly selected from the unit interval [0, 1]. Consider the random variable Y = (1-X)-¹/2 (a) Sketch Y as a function of X. (b) Find and plot the cdf of Y. (c) Derive the pdf of Y. (d) Compute the following probabilities: P(Y > 1), P(3 < Y < 6), P(Y ≤ 10).Let X1, X2,...,X, be a random sample from a distribution with density function e if x > 0 f(x; 0) elsewhere What is the maximum likelihood estimator of 0 ?b) The probability density function of random variable X is given as: - Вх {*5 if 0 < x < 1 otherwise f(x) = If the expected value of the random variable X is 1/3. Find the values A and B.Let Y1, Y2,., Ya be a collection of independent random variables with distribution function y 8 Show that Y converges in probability to a constant, and provide that constant. 1Recommended 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