Random variables and discrete probability distributions.
In this section you learned about random variables and discrete probability distributions.
• In this section we learned about random variables. Fill in the definition:
Random variable: _____________ Random variables are usually denoted by capital letters such as X. We usually use the abbreviation rv to stand for random variable.______________________________________________,
so its value is determined by chance.
o Looking at this definition, explain why “gender” cannot be a random variable.
___________________gender cannot be a random variable because gender cannot be count ____________________________________and measured. __________________
• All random variables are either discrete or continuous. Discrete random variables usually arise from counting while continuous random variables usually arise from _measurement ________________
• When we start doing inferences, we are going to need to be able to determine if an event is unusual. For now, we have defined an unusual event to an event whose probability is less than or equal to ____
• A value of the random variable X is unusually high if P( the variable has a value of x or more ) ___<=__ 0.05
• A value of the random variable X is unusually low if P( the variable has a value of x or less ) ___<=__ 0.05
Fill in the following as you work through your given problems in MyOpenMath.
1. a. rv X = _________________ the number of days it takes to fix defects in a randomly chosen pair of eyeglasses_________________________________________________
b. Just make a quick sketch of the probability histogram.
__________________________________________________________
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
What shape does the histogram above most resemble? ___Right-skewed______________________________
c. __mean____ = ___________________ ____days_________ (symbol, value, units)
Interpret this value in the context of this problem: ____mean number of days to fix defects = 4.204 days _________________________________
_______________________________________________________________________________
d. __Standard deviation____ = ___________________ __days___________ (symbol, value, units)
e. P( x>=15 ) = __0.007_______________________
f. Is 15 an unusually high number of days to fix a defect? ____ ____. Why or why not?
_____________________ because P(X>=15)<=0.05__________________________________________________________
2. If you flip a coin 3 times and list all of the possible outcomes of Hs and Ts you will get 8 total outcomes.
List them as the sample space: S = { HHH , HTH , THT ,THH , HHT , HTT , TTH , TTT }
a. rv X = __________ the number of heads flipped when you flip a coin three times________________________________________________________
Is this random variable discrete or continuous? ___ ____________________
b.
X P(X)
0 0.125
1 0.375
2 0.375
3 0.125
c. Just make a quick sketch of the probability histogram.
What shape does the histogram most resemble? ____ ____________________
0 1 2 3
d. ___mean___ = __________________ ___ __________ (symbol, value, units)
Interpret this value in the context of this problem: ___ If you flip a coin 3 times over and over, you can expect to get an average of 1.5 heads for every 3 flips__________________________________
e. __ ____ = 0.866 _____________ (symbol, value, units)
f. P( X>=2 ) = ________________________
3. This one helps to organize the info in a table like Table #5.1.6 on page 149.
a. Write the probability distribution of the player’s winnings.
Event X P(X)
losing -1 0.9999
winning 2099 0.0001
b. What is the expected value (with units)? __________________________ ___dollars___________
c.Interpret this value in the context of this problem: ____ _________________________________
4. This one helps to organize the info in a table like Table #5.1.6 on page 149.
(Keep in mind that if you have to replace the dishwasher, you will get another one for “free”)
a. Write the probability distribution of the
Event X P(X)
-112.10 0.86
887.9 0.14
b. What is the expected value (with units)? __________________________ ___dollars___________
c.Interpret this value in the context of this problem: _______________
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