Example 9.2.5 The pdf of a random variable X is assumed to be of the form f (x) = cx*, 0 s xs 1 for some number and constant c. If X, ...,X, is a random sample of size n, find the maximum likelihood estimate of a.

Q: A random variable Y has a uniform distribution over the interval (?1, ?2). Derive the variance of Y.…

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Q: EX7.8) Let Y be a random variable having a uniform normal distribution such that Y~U (2,5) Find the…

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Q: 1.4 Let X be a continuous random variable with pdf, fx(x), and fx (t+5) = fx (5 t) for all t> 0.…

A: Here, we have given a continuous random variables and also some condition is given. Then, we have to…

Q: Obtain maximum likelihood estimate of 0 in f(x, 0) = (1 + 0) x®, Example 0<x<1, based on an…

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Q: Question B) If the joint pdf of the continuous random variables X and Y is: fxy(x, y) = XY for 0<x<2…

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Q: Q3. The moment generating function for a random variable X is e3t M(t)=1-t2¹ What are the mean and…

A: The moment generating functionMx(t)=e3t/(1-t2)    -1&lt;t&lt;1To find mean and variance of X Concept…

Q: Let the random variable X have the moment generating function e³t M(t) = 1-t²-1<t<1 What are the…

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Q: Prob. 3 Let X be a random variable with cumulative distribution function (cdf) given by Fx(x) = {1 -…

A: Let X be a random variable with a cumulative distribution function (cdf) given byTo findThe…

Q: (i) the maximum value of p.d.f. (ii) expectation of X, E(X) (iii) variance of X.

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Q: Example 17-27. Let X1, X2, . X, be a random sample from uniform U[0, e], 0 > 0 ... population. Show…

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Q: B) Let the random variable X have the moment generating function e3t M(t) 1- t? for -1<t < 1, What…

A: Solution

Q: Example 9.2.6 Find the maximum likelihood estimate of the parameter i of the Weibull distribution…

A: Answer: For the given data,

Q: Example 13: Obtain the maximum likelihood estimator for 0 ofn random sample values from a uniform…

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Q: Three zero mean, unit variance random variables X, Y, and 2 are added to form a new random variable,…

A: Random variables and  have zero mean and unit variances.That is:  and These variables are added to a…

Q: Example 9.2.8 The lifetime of a device has a pdf fV) = 3a°y-4 yz a %3D For a random sample of size…

A: Answer: For the given data,

Q: Example 5-5. The diameter of an electric cable, say X, is assumed to be a continuous random variable…

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Q: If X₁, X2, ..., Xn constitute a random sample of size n from an exponential population, show that X…

A: let X1, X2, ......Xn is an independent identically distributed random variable following an…

Q: Question 23. (a) Use the expectation operator to show that for any random variable Y, Var(Y) = E(Y²)…

A: Solution: Part a) Variance is defined as the average of the squared differences from the mean. That…

Q: continuous random variables Z is known to have an Erlang (2,1.3) type PDF. what is the variance of Z

A: Given that Z is a continuous random variable having a distribution Erlang with parameters (…

Q: Example 6: Let x1, X2 , .., (0, 0). Find a sufficient estimator for 0. , Xn be a random sample from…

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Q: Example 5.4 Consider a random sample (X1. X2..X) from an exponential dis- tribution with parameter…

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Q: Example 9.2.9 (i) A sample of n independent observations is drawn from the rectangular population…

A: Answer: For the given data

Q: Find the covariance and the correlation coefficient between X and Y, if X and Y are jointly discrete…

A: For the given data Find the covariance and correlation between x and y

Q: (16) The moment-generating function of the geometric random variable X with parameter p is M(t) =…

A: The moment-generating function of random variable X is given as, M(t)=p1-1-pet It is known that…

Q: If a random variable X has the moment generating function Mx (t) = 2 - ť Datermine the variance of…

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Q: Example 2.14. Show the CDF of the random variable X with the following pdf: fx(#) =0.2(#)

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Q: 3. Let the random variable X have the moment generating function M(t) = -1 < t < 1. 1- What are the…

A: The MGF of the random variable  X is :M(t)=e3t1−t2−1&lt;x&lt;1Objective: Find Mean and variance of…

Q: Example 10 : If X is a continuous random variable and Y = aX + b, prove that = a E(X) + b and V(Y) =…

A: It is given that Y=aX+b.

Q: If a random variable X has the moment generating function M,(t) = %3D 2-t' determine the variance of…

A: Given,Mx(t)=22-t

Q: Example 3.17 Let X be a discrete random variable with range Rx = {0, 5,5, , 7}, such that Px(0) =…

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Q: 7. (a) Let x1, X2, , Xn be a random sample from the uniform distribution -0, dsewhere .... with…

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