Download Random Variable Mixed Practice Example 1

Random Variable Mixed Practice
Example 1: We’re playing a dice game. If you roll a 1, 2, or 3 you get no points. If you roll a
4 or 5 you get 5 points. If you roll a 6 you get 50 points.
a. Create a probability model where X = number of points won.
b. Calculate the expected value & standard deviation of X. Show all work.
c. What if we add 10 points, so that now you’d win 10 points, 15 points or 60 points?
What are the new mean and standard deviation? (Do not recalculate 𝜇𝑋 and 𝜎𝑋 here,
instead think of how the mean and standard deviation are affected by adding 10 points to
every value.)
d. What if instead of adding 10 points, we double the number of points you can win? What
are the new mean and standard deviation?
e. What if you play the game (with the original amount of points from part a) three times?
What is the mean and standard deviation of Y, playing three times?
Example 2: The American Veterinary Association claims that the annual cost of medical
care for dogs averages $100 with a standard deviation of $30, and for cats averages $120
with a standard deviation of $35. The annual costs for each animal are independent of
each other, and both the cost for dogs and the cost for cats follow a Normal model.
a. Describe the distribution of Y = the annual cost for a person who has one dog and one
cat.
b. What is the probability that the person who ones one dog and one cat will have to pay
more than $300?
c. A couple owns 4 dogs. What’s the expected medical cost? Standard deviation?
d. The American Veterinary Association decides that due to inflation, they will triple the
cost of medical care for cats. What’s the new expected cost and standard deviation for one
cat?
e. Based on the original expected value and standard deviation, what is the probability
that a dog’s annual expenses will cost more than a cat’s? (This is similar to the speed
dating problem we did in class on Friday).