Question

In: Statistics and Probability

Use MATLAB to plot the likelihood function for estimating the probability of a coin landing heads-up...

Use MATLAB to plot the likelihood function for estimating the probability of a coin landing heads-up without prior knowledge after observing HTHT. -would greatly appreciate if you went in detail on how to find the likelihood function based off the given information.

Expert Solution

Let p be the probability of landing Heads up.

Let be the independent outcomes from n toss of a coin, taking the value 1 if it lands heads up and 0 otherwise.

Then has a Bernoulli distribution with parameter p with probability

The joint probability of observing and hence the likelihood is

We wanve observed HTHT. That means n=4.

The likelihood of observing HTHT is

We will plot L(p|x) for different values of p=[0,1] and find the value of p at which the likelihood L is the maximum.

Matlab code

The plot is

We can see that the maximum is at p=0.50.

the output from the program confirms that

The maximum likelihood estimate of p (the probability of a coin landing heads up) given the sample HTHT is

orchestra answered 2 years ago

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