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.
1. Construct the
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
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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