Every time that its arm is pulled, a slot machine yields a reward which is Gaussian distributed N(YTRUE, 1), i.e., with mean YTRUE and variance 1. The successive pulls are independent. The value YTRUE is not known; all that is known is the that slot machine yields a reward N(y, 1) for some value of y. The slot machine is played m times, and the results are recorded as a vector (x1, x2, ,m), where x; is the reward obtained on the i-th play of the slot machine. (i) What is the probability of obtaining x for a given y? (i) Determine the Maximum Likelihood estimate hML of yTRUE. (ii) Is the Maximum Likelihood estimate of YTRUE unbiased? (iii) Does the Maximum Likelihood estimate converge in probability to YTRUE as m ?