Consider a univariate normal model with mean mu and variance tau. Suppose we use a Beta(2, 2) prior for mu (somehow we know n is between zero and one) and a log-normal(1, 10) prior for tau (recall that if a random variable X is log-normal(m, v) then log X is N(m, v)). Assume a priori that mu and tau are independent. Implement a Metropolis-Hastings algorithm to evaluate the posterior distribution of mu and tau. Remember that you have to jointly accept or reject mu and tau. Also compute the posterior probability that mu is bigger than 0.5. Here are the data: Attempt: (Heres to enter my data) mu <- rbeta(l, 2, 2) tau <- rlnorm(1, 1, 10) x <- c(2.3656491, 2.4952035, 1.0837817, 0.7586751, 0.8780483, 1.2765341, 1.4598699, 0.1801679, -1.0093589, 1.4870201, -0.1193149, 0.2578262)