Question

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.

Answer 1

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.