Question is on attached file. I will accept answer if you can complete at least 3 questions.

Problem 1 Suppose 1059 primary school children {aged Er - 12 years old ]I in Australia were randomly selected and asked if they had their own personal iPad. Among this group of children, 691 of them said that they had their own personal iPad. Alex and Bob both want to use the binomial model as the sampling model assumption for this data set1 but they have different prior beliefs about 3. the proportion of primary school aged children in Australia who have their own personal iPad. {a} Alex thinks that the expected value of H is around ELSE. Design a continuous beta prior distribution that reects Alex's belief. (bl Bob thinks that the median value of H is around [Le-'5 and the 90th percentile is around [135. Design a continuous beta prior distribution that reect's Bob's beliefs. (Note: you may nd the function beta.eelect in the LearnBayes package helpful to set Bob's prior distribution assumption. Sec h1'.'l:.ps:.I"';I"rd:r:r.1o.II'oranin"LeEurasiaswear"mart.IF beta. so leer. .html] {c} Derive Alex's posterior distribution and Bob's posterior distribution of I9. {d} Plot the tum priors on one graph. and plot the corresponding posteriors on another graph {e} l[:J'btain 95% posterior credible intervals for I? for Alex and Bob respectively. {E} For each person is the prior distribution assumption consistent with the observed data? Explain your answer. {H.int: you might want to run some prior predictive checks which are similar to posterior predictive checks but based on the prior predictive distribution pfyl)