Research Statistics 2
Video Worksheet to Accompany “Random Variables”
Unit 1
https://www.learner.org/series/against-all-odds-inside-statistics/random-variables/
Unless you’re asked to write an equation or perform a computation, you should write your
responses in
clear, grammatically correct sentences.
1. Define random variables. Correct
a. The numerical outcome of a random phenomenon.
2. Give an example of a random variable that does not involve coins, dice, or spinners –
one that is drawn from everyday life. (Define it precisely, so that anyone could measure
your variable.) Correct
a. Suppose the maximum number of items in someone’s Amazon cart is 5. A
random variable is the number of items added to the cart by Amazon
customers.
3. What are the two essential elements of a probability distribution of a (discrete) random
variable? Correct
a. The two essential elements are the possible values of the random variable
and the probability of each possible value.
4. Create a probability distribution for the random variable you created in question 2. You
can, of course, assume you’ve observed many, many outcomes of the random
phenomenon, but your made-up probability distribution should be plausible. Correct
a.
X
1
2
3
4
5
P(X)
0.24
0.10
0.21
0.21
0.24
b.
5. Identify similarities and differences between a probability histogram and a histogram
made to show the distribution of a quantitative variable. Correct
a. A probability histogram is typically used for discrete random variables and
is only sometimes used for a continuous random variable. A histogram
made to show the distribution of a quantitative variable can be used with
both continuous variables as well as discrete variables. A probability
histogram can be made from a theoretical model and the area of the
histogram is always equal to one, while the area of the histogram made to
show the distribution of a quantitative variable is proportional to the
number of observations it represents.
6. What was the main statistical flaw in the safety calculation made by NASA to assess the
safety of the field joints in the space shuttle? Correct
Note: The error of assuming probabilities are independent when they are not occurred in
courtroom arguments in the UK (late 90’s) and California (1960’s). You can read about
the cases of Sally Clark and Janet Collins in the first 2 chapters of Math on Trial.
http://e.guigon.free.fr/rsc/book/SchnepsColmez13.pdf
a. The O-rings were not independent which caused the failure. NASA
assumed the field joints were independent of each other but this was not
the case.