(Solved): Suppose that X is a discrete random variable with the following probability mass function: where 0 ...

Suppose that $$X$$ is a discrete random variable with the following probability mass function: where $$0???1$$ is the parameter. A random sample of sequence of 10 i.i.d observations from the distribution were as follows: $$(3,0,2,1,3,2,1,0,2,1)$$. 1. Write out the likelihood and log-likelihood functions. 3. Use calculus to derive the maximum likelihood estimator of $$?$$. 4. Calculate the the maximum likelihood estimate using the data provided. Example 1: Car Ownership. You are tasked with estimating the proportion of UoG undergraduates that own a car. Suppose we have a random sample $$X_1,X_2\dots X_n$$ where $$X_i=1$$ if a randomly selected student does own a car and $$X_i=0$$ if a randomly selected student does not own a car. Assume that the $$X_i$$ are independent and identically distributed Bernoulli random variables with unknown parameter $$?$$. Find the maximum likelihood estimator of $$?$$, the proportion of students who own a car.