Question

Suppose that random variables X1, · · · , Xn are independently from the uniform distribution on [a, b]. Find the MLE of the mean of the distribution.

Answer 1

To find the MLE of the mean of the given distribution, calculate the likelihood function, maximize it, and solve the resulting equation.

Step-by-step explanation:

To find the maximum likelihood estimator (MLE) of the mean of the distribution, we need to calculate the likelihood function and maximize it. Since the variables X1, ..., Xn are independently and uniformly distributed on [a, b], the likelihood function is given by:

L(μ) = f(x1; μ) × f(x2; μ) × ... × f(xn; μ) = 1 / (b - a)n

To maximize the likelihood function, we take the derivative with respect to μ and set it equal to zero:

dL(μ) / dμ = 0

Solving this equation will give us the MLE of the mean of the distribution.