Rejection sampling and importance sampling: Consider the model, yjâ¼Binomial(nj,θj),whereθj= logitâ1(α+βxj), forj=1,...,J, and with independent prior distributions,αâ¼t4(0,22)andβâ¼t4 (0,1). SupposeJ=10,thexjvalues are randomly drawn fromaU(0,1) distribution, andnjâ¼Poisson+(5), where Poisson+is the Poisson distributionrestricted to positive values.(a) Sample a dataset at random from the model.(b) Use rejection sampling to get 1000 independent posterior drawsfrom(α,β).(c) Approximate the posterior density for (α,β) by a normal centered at the posteriormode with covariance matrix fit t