Educ 603 (Probability Theory for Teachers)

Quiz 06 - Chapter 6

This quiz covers topics discussed in Chapter 7 (pages 70-80 of Gravner). Show any andall solutions.

1. 5 pts. Consider the experiment of throwing a fair six-sided die and tossing a faircoin simultaneously.

(a) List five elements of the sample space.

(b) Let X be the number of heads showing on the coin and Y be the number showingon the die, i.e., X ∈ {0, 1} and Y ∈ {1, 2, 3, 4, 5, 6}. Find FXY = 1.

2. 20 pts. A fair coin is tossed 4 times. Let the random variable X denote the numberof heads in the first 3 tosses, and let the random variable Y denote the number ofheads in the last 3 tosses.

(a) What is the joint probability mass function (pmf) of X and Y ?

(b) Find the probability that 2 or 3 heads appear in the first 3 tosses and 1 or 2 headsappear in the last 3 tosses.

(c) What is the joint cumulative distribution function (cmf) of X and Y ?

(d) Compute the probability that less than 3 heads appear in both the first and last3 tosses.

(e) Find the probability that 1 head appears in the first three tosses.

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