Reference no: EM13836345
Question 1: Assume we have an i.i.d. sample from Bernoulli random variable, specifically X1, X2... ,Xn ~ B (p), which means
f (Xi) = pxi (1 - p)1 - xi, Xi = 0, 1.
In class we showed that
Is a stationary point for the likelihood for the parameter p. Show p indeed maximizes the likelihood?
(Hint: find the second derivative d2/dp2 log L(p¦X1, ... , Xn), and show that it is negative at p)
Problem 2: Assume the random variable X follows the exponential distribution through the following parameterization of its probability density function
f (x) = Θe -Θx, for x ≥ 0.
If you have and i.i.d sample X1, X2, ... , Xn from this distribution, what is maximum likelihood estimator for Θ?
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