all parts please Suppose that we have data y = (y₁,...,yn). Each data-point y; is assumed to be generated by adistribution with the following probability density function:8²p(y; | 0) = = = = exp( - ), y₁ ≥ 0.The unknown parameter is 0, with 0 > 0.(a) Write down the likelihood for given y. Find an expression for the maximum likelihoodestimate (MLE) 8.(b) A Gamma(a,ß) distribution is chosen as the prior distribution for 8. Derive the resultingposterior distribution for 8 given y.

a) The likelihood function for the parameter θ given the data y can be written as follows:The…

Suppose that we have data y = (y1,...,yn). Each data-point y; is assumed to be generated by a distribution with the following probability density function: p(y₁|0)== - 1/7 exp(-2) ₁ 31₁ 2 0. The unknown parameter is 0, with > 0. (a) Write down the likelihood for @ given y. Find an expression for the maximum likelihood estimate (MLE) 8. (b) A Gamma(a,ß) distribution is chosen as the prior distribution for 8. Derive the resulting posterior distribution for given y.

Suppose that we have data y = (y1,...,yn). Each data-point y; is assumed to be generated by a distribution with the following probability density function: p(y₁|0)== - 1/7 exp(-2) ₁ 31₁ 2 0. The unknown parameter is 0, with > 0. (a) Write down the likelihood for @ given y. Find an expression for the maximum likelihood estimate (MLE) 8. (b) A Gamma(a,ß) distribution is chosen as the prior distribution for 8. Derive the resulting posterior distribution for given y.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 7CR

See similar textbooks