Intro to Econometrics

This question will cover statistical inference, the relationship between a population parameter and the sampleaverage.

Suppose you toss a coin and are interested in the probability of have a head. Assuming the coin is not rigged, the random variable X defined as 1 if it is a head and 0 if it is a tail is described by a Bernoulli distributor which takes the value 1 (head) with the population probability p = 0.5

1. What is the probability of having a tail? What is the expected value (population mean) of X? What about the population variance? Write down the formula first and then calculate the value.
2. Generate a sample of N = 10 observations from randomly drawing from the coin experiment in R, i.e., {X1, X2,...,XN}