Muffin is a cute dog that barks 80% of the times someone calls his name. The event that Muffin barks when his name is called, is independent of him barking or not barking in the past.

One day his owner tried to do the following: she called his name 3 times keeping record of how many times he barked. After these 3 times, she gave him treats. The number of treats she gives him is square the number of times he barked. For example, if Muffin barked only in the first and last time his name was called (and didn't bark in the second time), he received 4 treats (as 4=2².)

Let X be the random variable that denotes the number of treats Muffin gets.

a. Find the distribution of X. That is, for each possible value of X, say what is the

probability X would get that value.

b. What is E(X)? Tat is, find the expected value of X.

Explain your answers.