You go to a casino and play a game until you observe your rst victory. Denote by X the Geometric random variable associated with the number of times it takes for you to see your rst victory. If your chances of winning are given by p and every time you play the game is independent of the previous times, then PlX = :13] = (1 p)(m'1)p~ However, you now are not sure about your chances of winning, so you plan to estimate that after observing the data. Let X, denote the geometric random variable associated with the number of times you played the game at night 1'. After a week playing the same game every night until you win for the rst time, you observe the following random sample of independent draws from this geometric distribution: X = (10,9,11,8,12, 10,10). a) Write the likelihood function of the parameter p given the data. b) Find the maximum likelihood estimate of p. c) Write down the formula/ expression for the probability of observing this dataset X : (10,9,11,8,12,10,10) when p z 99%. Is the chance of observing this dataset high when p z 99%? Explain your