Consider an experiment which consists of 2 independent coin-tosses. Let the random variable X denote the number of heads appearing. Write down the probability mass function of X.

There are 10 balls in an urn numbered 1 through 10. You randomly select 3 of those balls. Let the random variable Y denote the maximum of the three numbers on the extracted balls. Find the probability mass function of Y . You should simplify your answer to a fraction that does not involve binomial coefficients. Then calculate: P[Y 7].

A fair die is tossed 7 times. We say that a toss is a success if a 5 or 6 appears; otherwise its a failure. What is the distribution of the random variable X representing the number of successes out of the 7 tosses? What is the probability that there are exactly 3 successes? What is the probability that there are no successes?

The number of misprints per page of text is commonly modeled by a Poisson distribution.It is given that the parameter of this distribution is = 0.6 for a particular book. Find the probability that there are exactly 2 misprints on a given page in the book. How about the probability that there are 2 or more misprints?