Quiz 7 a

1. Give an example of a random variable.

Remember that a random variable is a random, *numerical* outcome of an experiment.   So your answers should have an experiment mentioned, and the outcome should be (a) random and (b) numerical.  The most common mistake was to describe non-numerical variables.  The second most common mistake was to give a vague, sometimes impossibly vague, description of the experiment.


Here are some sample answers from class:
•  Whether or not you get in a car accident
        First -- there's no experiment.  We could create one by saying "when you drive home tonihgt" or "in your lifetime" or something that gives us a period of observation.  Second, the outcome, while random, is not numerical.  We could improve it by saying, "a 1 if you get in an accident, and a 0 if not."
        So an improved version:  X is a random variable that is a 1 if you are in a car accident anytime before midnight tonight, and a 0 otherwise.
Let's hope for 0's.

• The height of a person in the US that you will choose at random.
    Got the experiment--- choose a person.  Got the randomness -- while one's height is not random, choosing a person at random means that the height we choose is random. And got the number.  A near-perfect answer.  Could be made more precise by saying "heihgt in inches" for example.

• A card chosen out of a deck of normal playing cards.
    We've got an experiment with a random outcome, but the outcome is not numerical.  Maybe if we said "the numerical value of a card chosen at random, where Jack, Queen, King = 10, Ace = 1."

• conducting an experiment on how many teenage girls get pregnant before the age of 16.  Asking random 16 year olds or younger girls.
The experiment is a little fuzzy.  We could fix this up by saying "Take a random sample of 16 year olds and ask if they've been pregnant."  The numerical outcome, then, is the number of girls in the sample who answer "yes".

• If parents are trying to have kids but want a girl, then the expected number of tries before having a girl is 6 and the random variable would be girl or boy.   
    Here's its not clear what the experiment is.  Is it having a single child?  Having 6 children?  And its not clear where the 6 comes from.  It is clear that the outcome "girl or boy" is not numerical.  This could be fixed by saying "the number of girls in a randomly selected family of 6 children."

• Drawing the top card from a newly shuffled deck of cards.  Having to guess the color outcomes (black or red) provides the variable. Again, no numerical value.