3. A coin is flipped twice. Let Y = number of heads obtained, when the probability of a head for a flip equals . (6 pts each) (a) Assuming = 0.50, specify the probabilities for the possible values for Y, and find the distribution's mean and standard deviation. (b) Find the binomial probabilities for Y when equals 0.55. (c) Suppose you observe y = 1 and do not know . Calculate and sketch the likelihood function. (d) Using the plotted likelihood function from (c), show that the ML estimate of equals 0.50. (e) Refer to the previous exercise. Suppose y = 0 in 2 flips. Find the ML estimate of . Does this estimate seem "reasonable"? Why? 4.A Poisson regression model was fitted to data on train accidents in the UK between 1975 and 2003. [Hint: Use the formulas given to compare Poisson GLM.] (10 pts each} 3 Formulas [ln()]=111+1211(11+12)1(21+22) To compare two Poisson models Use Devianceo - Deviance1 and has chi-squared distribution with df =1. z = /SE, z2 has 2 with 1 df.