Simulating from a beta curve

Suppose Rebekah's beliefs about the proportion P of female students who think they are overweight is modeled by a beta curve with parameters 24.13 and 7.67.

Suppose you make 1000 draws from Rebekah's posterior curve using the rbeta() function.

The hist() function can be used to construct a histogram of the simulated values, upon which you can place the beta curve.

p_sim <- rbeta(1000, 24.13, 7.67)
hist(p_sim, freq = FALSE)
curve(dbeta(x, 24.13, 7.67),
      add = TRUE, col = "red", 
      lwd = 2)

You can perform different inferences about the proportion P by summarizing this sample of simulated draws.

Instructions

Summarize Harry's posterior density for P, which is beta with parameters 19 and 7.

Define the vector ab, the beta shape parameters for Harry's posterior.
Use the rbeta() function to simulate 1000 values from this beta curve. Store the values in p_sim.
Construct a histogram of the simulated values.
From the simulated values, compute the probability that P is larger than 0.7.
Use the simulated values and the quantile() function to compute a 90% Bayesian probability interval.

Take Hint (-30xp)