Verify that this is a probability distribution

1. Typographical errors such as when “the” is spelled as “teh” are referred to as non-word errors. When undergraduates are asked to write a 250-word essay (without using a spell-check) the number of non-word errors has the following distribution:

(a) Verify that this is a probability distribution. HINT. Remember you must show that two conditions are satisfied. One of these conditions (that all probabilities are positive is already given).

(b) Compute the mean number of non-word errors in an essay.

2. In the following situations is it reasonable to use the binomial distribution?

(a) A coin is tossed until a head appears. Let  be the count of the number of tosses made.

(b) A survey call reaches a live person or does not. The researcher conducting the survey calls 600 people in a city. Let  be the number of times a live person is reached.