12.45 Spelling errors. Spell-checking software catches “nonword errors” that result in a string of letters that is not a word, as when “the” is typed as “teh.” When undergraduates are asked to type a 250-word essay (without spell-checking), the number X of nonword errors has the following distribution: Value of X 01234 Probability 0.1 0.2 0.3 0.3 0.1

(a) Is the random variable X discrete or continuous? Why?

(b) Write the event “at least one nonword error” in terms of X. What is the probability of this event?

(c) Describe the event X $ 2 in words. What is its probability? What is the probability that X ( 2? 12.46 First digits again. A crook who never heard of Benford’s law might choose the first digits of his faked invoices so that all of 1, 2, 3, 4, 5, 6, 7, 8, and 9 are equally likely. Call the first digit of a randomly chosen fake invoice W for short.

(a) Write the probability distribution for the random variable W.

(b) Find P1W & 62 and compare your result with the Benford’s law probability from Example 12.7.