1. Construct the probability distribution for each discrete random variable. a. Sum of the outcomes when the two dice are rolled. b. Number of girls in a family with 3 children. c. Product of two numbers taken separately from two boxes containing number 1, 2, 3, and 4.

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1. Construct the probability distribution for each discrete random variable.
a. Sum of the outcomes when the two dice are rolled.
b. Number of girls in a family with 3 children.
c. Product of two numbers taken separately from two boxes containing number 1, 2, 3, and 4.
d. Sum of 3 numbers taken separately from 3 jars containing 0, 1, and 2.
2. Suppose Mary has yoga classes 3 days in a week. She attends classes 3 days a week 80% of
the time, 2 days 15% of the time, 1 day 4% of the time and is absent for the week 1% of the time.
Let X be the number of days Mary is present in a week.
a. Construct the probability distribution of X in a tabular form.
b. What is the probability the Mary will be absent for at most 2 days?
c. Compute the mean and standard deviation of X.
3. Consider drawing 2 balls at random with replacement from a jar containing 2 black balls
and 4 white balls. Let X be the number of black balls selected.
a. Construct a table giving the probability function of X.
b. What is the chance of picking at most 1 black balls?
c. What is the chance of picking at least 2 black balls?
d. Compute the mean and standard deviation of X.
4. A biased coin with probability of 0.7 for a head (in one toss of the coin) is tossed 5 times. Let
X be the number of heads.
a. Construct a table giving the probability function of X.
b. What is the probability of observing 4 heads?
c. What is the probability of observing at least 3 tails?
d. What is the probability of observing greater than 2 head?
e. Compute the mean and standard deviation of X.
5. A blindfolded marksman finds that on the average, he hits the target 4 times out of 5. If
the fires 4 shots,
a. Construct a table giving the probability of number of times he hits the target.
b. what is the probability of 3 hits?
c. what is the probability of more than 2 hits?
d. find its mean and standard deviation.

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