Mathematics

Carolina Gilmore

1 January, 10:32

So I have this exercise and don't know how to approach it:

You ask five students to toss a coin 10 times and to report k, the number of times heads faces up in the sequence of ten tosses. The obtained data are displayed in Table 1.

student 1 - k=8

student 2 - k=8

student 3 - k=5

student 4 - k=4

student 5 - k=6

From these data, this is the 5 observations of k in Table 1, derive the maximum likelihood estimator for π, the probability of heads.

1. Formulate the data generating model.

2. Formulate the objective function (use maximum likelihood estimation). Make a plot of the log-likelihood function for the reported data set (in R).

3. Solve the optimization problem. Report the estimator and show the steps you took to find this estimator.