2. This problem will lead you through the steps of determining the probability distribution, mean, and variance of the random variable 'x, the sample mean. Consider the population made up of only three individuals with corresponding values 1, 2, and 4. The specific sampling procedure you will use involves randomly selecting a sample of size n = 2 from the population with replacement. Sampling with replacement means that each time an individual is drawn from the population, its value is recorded and then the individual is returned to the pool of individuals available selection on the next draw. (a) First, consider the scenario where a single individual is selected from the population at random. Define the random variable X as the observed value of the one selected individual. Write out the possible values of X and their associated probabilities in the form of probability distribution table. Then calculate the mean, pX, and standard deviation, 0X. uX = 713 O'X = 1.2472