Parameter Learning: Beta distribution

[2 P]You want to estimate the bias of a coin using a Bayesian approach. For that you toss the coin ten times and get the following result

$\{h,t,t,t,h,t,h,t,t,t\}$

a)

Compute the parameters of the posterior probability using a uniform Beta distribution as prior. Plot the posterior probability density function using the MATLAB function betapdf.

b)

You do another experiment with ten tosses and this time you get the following result

$\{h,h,t,h,t,t,h,t,t,h\}$

Again compute the parameters of the posterior probability with (i) a uniform Beta distribution (ii) using the parameters you obtained after the first experiment. Plot the two posterior probability density function.

c)

Compute the probability that the next toss will be $h$ using the results from b).

d)

Explain the different results you get in b) and c).