Note: For the purposes of this assignment, if X is a random variable we let px denote the probability density function [pdf) of X, Fx to denote it's cumulative distribution function, and P to denote probabilities. These can all be related as follows: E P[X S r) = Fx[r) 2/ pX[z)dz 00 6 Po. 3 X <_: b fxs fxm px . often we will simply write as p where it clear what random variable the distribution refers to. you should show your derivations but may use a computer algebra system to assist with integration or differentiation. are not assessing ability integrate f differentiate herel would now like investigate posterior distributions obtained function of parameters and b. credits briefly comment about how camera behaves for each these cases expect this change agent updates prior on given an observation x equations required. shouldn need any assumptions question. compute all e errors made by i.i.d in that past outputs do affect future outputs. c coin is flipped reports seeing one. arbitrary does simplify when explain observations. d uniform under assumption :="a." let plot same graph compare them. shape changes o. have bayesian running trying learn information pa- rameter could be ip problem based observations through noisy camera. takes photo back if result was unfortunately perfect sometimes wrong value probability makes mistakes controlled two control likelihood correctly reporting zero one respectively. letting denote true outcome denoting reported can draw relationship between shown. so pl="0|X=1)=1">