Suppose that we have data y = (y₁, ... ,yn). Each data-point is assumed to be generated by a distribution with the following probability density function: p(y¡ | 4) = 24y¡ exp(−¥y?), y¡ ≥ 0, i = 1,...,n. The unknown parameter is , with > 0. Write down the likelihood for given y. Find an expression for the maximum likelihood estimate (MLE) .

Q: The random variable X is normally distributed such that X~N(?, 12). It is known that ?(? > 32) =…

A: It is given that the probability of x greater than 32 is 0.0618. and the standard deviation is 12.

Q: X₁~N(0,1),i=1,..., n and they are independent of each other, then X₁ + X ( ) distribution.

A: Given that, they are independent of each other.We are asked to find the distribution of .

Q: Let Y be a continuous random variable that is normally distributed with mean, u = 30 and standard…

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Q: 10. Let F(x) - cumulative distribution function of the random variable . Find the cumulative…

A: Given that, F(x) is the cumulative distribution function of the random variable ξ.

Q: Let Y. Y. Y, be the order statistics of a random sample of size 3 from a beta distribution with…

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Q: Q2: Let X and Y have a bivariate normal distribution with parameters 4, H2 1,of = 16, a = 25 and p=…

A: Solution

Q: The time it takes me to ride my bike to school is uniformly distributed between 20 minutes and 36…

A: We have find uniform distribution...

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A: The question is about normal distribution Given : Popl. mean pulse rate of females ( μ ) = 76 beats…

Q: Assume that IQ scores are normally distributed with a mean 98.3 pts and a standard deviation of 10.2…

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Q: Give the formula for calculating the quartiles, of a continuous distribution.

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Q: The probablity density function takes a value of between 10.7 and 11.7 ounces and a value of…

A: Let X denote the weight of a can of soup. Given that X follows Uniform(a = 10.7, b = 11.7)

Q: Let X denote the distance (m) that an animal moves from its birth site to the firs territorial…

A: Answer Given X has exponential distribution with parameter =0.01337

Q: The lengths of a professor's classes has a continuous uniform distribution between 49.29 min and…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: X,,X2, ... ,X, is a random sample selected from the normal distributionx,~N(6,25) ·Ã and 52 is the…

A: There are nine random variables X1 , X2 ,....., X9 where Xt=N(6,25). The sample mean and sample…

Q: Let x be a continuous random variable that is normally distributed with a mean of 57 and a standard…

A: We have given that  Let x be a continuous random variable that is normally distributed with a mean…

Q: From a continuous uniform distribution, X ~ Unif[a, b], we are given the following set of data: 5,…

A: Given the set of data from a continuous uniform distribution : 5, 6, 8, 8, 9, 7, 2, 4, 6, 5.

Q: Suppose X has a continuous uniform distribution over the interval -1,1. Determine the variance.…

A: We have given that,  X be the continuous random variable from uniform distribution with a = -1 and b…

Q: The time to failure of a component is Weibull distributed with a scale parameter of 2000 hours,…

A: Given that the time to failure of a component is Weibull distributed with a scale parameter of 2000…

Q: 2. Let X be a random variable with the a normal probability density function (with known mean and…

A: We have given that X be a random variable with a normal probability density function ( known mean…

Q: Parts (a) and (b) are both related to normal distribution but are not directly connected to each…

A: a)Mean= -1 , Standard deviation = 2

Q: The median of the probability distribution of a random variable X is that value m which makes the…

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Q: I model the time at work as a Gamma distribution with parameters r = 20, = 2. What is the average…

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Q: If the random variable X has an exponential distribution with rate parameter A = 11.42 then, given…

A: We have given that λ = 11.42 We know that, Var(X2)= E(X4)-(E(X2))2 Given that X~exp(11.42) So…

Q: From a continuous uniform distribution, X - Unif[a, b], we are given the following set of data: 5,…

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Q: Find the following probabilities. It may help to sketch the pdf for Standard Normal Distribution and…

A: given data,we have to answer fisrt 6 subparts of the given data Z~ Norm(0,1)here for dtandard normal…

Q: X1,..,Xn random sample from gamma probability distribution with parameter a,b. Find moment…

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Q: EZ = X +Y if X,Y are

A: X follows normal distribution with mean 0 and variance 1. Y follows normal distribution with mean 0…

Q: Q3. Suppose that X¡, i = 1,2, ...,n have an Exponential distribution with parameter a. a) Find…

A: Introduction :-  Here the random variable follows exponential distribution with parameter lambda. We…

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Q: table below gives a discrete probability distribution x Pr(X=x) 1 0.1883 4 0.1618 7 0.1392 10…

A: Table that shows the necessory calculations is: X p(X)p(X) X \cdot p(X)X⋅p(X) X^2 \cdot…

Q: = 2) Let the joint probability function of X & Y be defined by Pxy(x, y) = Is this a proper…

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A: # Given: xi follow geometric distribution (p) :f(xi/p)=(1-p)^(x-1)*p  And prior distribution of p…

Q: 4. Let X1, X2, X3 .., X, are independent random variables from pdf f (x) corresponding to cdf F(x).…

A: U = min(X1, X2, X3, ..., Xn) V = max(X1, X2, X3, ..., Xn) W = V - U

Q: The orders from n= 100 customers for wooden panels of various thickness (X) are summarized as…

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