In this problem, we consider an application of posterior statistics. suppose that we have five loaded coins; the probability of each landing heads is 0.2 , 0.4 , 0.4 , 0.6 , and 0.8 . the coins are placed in a bag, and one coin is drawn completely at random. let the probability that the coin drawn comes up heads on a given toss be . our goal is to infer something about the probability that the coin picked will land heads, and we would extract information by flipping the coin times and recording the outcomes of the tosses. (a) preliminary ingredients 2 points possible (graded) in a bayesian model, given the description of the situation, what is the prior distribution of the parameter of interest , which we define as probability that the coin chosen lands heads? enter the prior probabilities for =0.2 , =0.4 , =0.6 , =0.8 , as a vector =0.=0.=0.=0.8)) . for example, if =0.2)=0.=0.4)=0.=0.6)=0.=0.8)=0.3, then enter [0.5,0.1,0.1,0.3]. note the components are separated by commas, and the vector is enclosed by square brackets. =0.=0.=0.=0.8))=from the posterior distribution, compute the posterior mean, mode, and median. posterior mean: posterior mode: posterior median