The Bayern Munich player Arjen Robben scores most of his goals with the left foot. The statistics of the goals he has scored by foot are as follows:

Let \(\pi\) be the proportion of Robben's foot scorings that he does with his left. Find the probability distribution of \(\pi\) when...

(a) you use Jeffreys' prior for proportions, and update the probability distribution for \(\pi\) with the observations from 2013/14;

(b) you go a new round, and update with the observations from 2014/15;

(c) you further update with the observations from 2015/16;

(d) What is the probability that \(\pi\) is in excess of \(75 \%\) ?

(e) Find the probability distribution of the number of left-foot goals in Robben's next 3 foot scorings.

(f) Find the probability that 2 out of the next 3 foot scorings are done with his left.

Transcribed Image Text:

Season left right 2013/14 9 2014/15 2015/16 12 12 3 1 20