| thank u morgaine300 for ur response and i am sorry if i make any mistake by saying that i needed my answer asap but i was excited yesterday when i found this website and i was looking forward to having my answer fast, any way these r my exercises i hope it is clear for all of u.
1. The table below records the sales of computer and printers by a retailer over 200 days.
Let the random variable X denote the number of computers sold, and the random
variable Y the number of printers sold.
X = 0 X = 1 X = 2 X = 3 X = 4
X
Y = 0 6 6 4 4 2 22
Y = 1 4 10 12 4 2 32
Y = 2 2 4 20 10 10 46
Y = 3 2 2 10 20 20 54
YX= 5 2 2 2 10 30 46
16 24 48 48 64 200
a. Create a table showing the joint probability of X and Y
b. Create a table showing the marginal (individual) probability of X and of Y
c. Are X and Y statistically independent? Explain your answer.
2.
a. Let the random variable X be equal to the number shown when tossing a die once. Plot
the probability mass function (PDF) of X.
b. Let the random variable X be equal to the sum of the numbers shown when tossing a die
twice. Plot the probability mass function (PDF) of X.
3. An automatic machine Â…lls plastic bags with a mixture of vegetables. Because of
variations in the size of the di¤erent vegetables, not all bags will contain the correct
weight, as speciÂ…ed on the package. A check of 4000 packs in the last month revealed
that 100 packages were underweight and 300 packages were overweight.
Evaluate the following probabilities:
a. what is the probability that a randomly selected package will be overweight?
b. what is the probability that a randomly selected package will be either underweight or
overweight?
c. Let event A correspond to the overweight outcome. Use a Venn diagram to show A and
~A.
4. Brie‡y (i.e. no more than 3 lines) but clearly de…ne/explain the following
1
Venn diagram
Joint probability
Conditional probability
statistical independence
Probability mass function
discrete random variable
2 | 
Linear Mode
