Question 14.1. Consider tossing a fair coin 3 times. The sample space would be: ={, , HTH, THH, HTT, THT, TTH, TTT} Let X represent the number of heads obtained. Calculate the corresponding probability density function x = (P(X = 0), P(X = 1), P(X = 2), P(X = 3))" Calculate the corresponding cummulative density function F. Use the PDF as well as the CDF to calculate P(X 1). Question 14.2. A fair six-sided die is tossed once. You win $2 if the result is a "1", you win $1 if the result is a "6" but otherwise you loose $1. Write down the probability density function for the random variable X = amount of money won or lost. Calculate the mean and the variance of X.