156k views
4 votes
Let X 1 …X n be a random sample from a population with common pdf: f(x)= θxe − 2ie 20(a) Find the likelihood and the log-likelihood function of θ.

1 Answer

6 votes

Final answer:

The likelihood function is obtained by multiplying the values of the common pdf at each data point. The log-likelihood function is obtained by taking the natural logarithm of the likelihood function.

Step-by-step explanation:

The likelihood function is given by multiplying the values of the common pdf at each data point. In this case, the likelihood function is L(θ) = θx1 + x2 + ... + xne-2θne-20θ∑i=1nxi.

The log-likelihood function is obtained by taking the natural logarithm of the likelihood function. Therefore, the log-likelihood function is log L(θ) = (x1 + x2 + ... + xn)ln(θ) - 2nθ - 20θ∑i=1nxi.

User Alvarez
by
9.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories