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Misc
Probability Distributions
Binomial
Geometric
WildCard
100

Discrete random variables are this, unlike continuous random variables

What is finite? (or countably infinite!)

100

To have a discrete probability distribution for X, all probabilities for each value of X must be between or equal to these two values.

Must be between 0 and 1.

100

What is the binomial coefficient for a scenario involving 50 trials and 8 successes?

536878650

100
This is the probability that the first success of a series of trials is on the 5th trial when the probability of success is 0.38.
What is 0.056 or 5.6%?
100

You shoot 50 free throws and count the # of free throws you made. Is this Binomial or Geometric?

Binomial. X = # of successes

200
The probability distibution that looks for the number of successes within a set number of trials.
What is a Binomial distribution?
200
If you have a discrete probability distribution, all probabilities must add up to this number.
What is 1?
200
The probability that a student answered yes to the question, "Do you do your homework?", is 4 out of 7. This is the probability that out of 100 students 43 said that they do their homework.
What is 0.069 or 6.9%?
200
The probability that a typical bag of potato chips is under filled is 68%. This is the probability that the first bag of potato chips bought from a vending machine that is under filled is the 6th bag of chips bought.
What is 0.0022 or .22%?
200

You are shooting free throws, and count the # of free throws it took for you to make one. Is this Binomial or Geometric?

Geometric. Counting the # of trials

300
The expected value of a probability distribution is equal to this.
What is the mean?
300

If the following is a discrete probability distribution, fill in the missing probability: 

0 - 0.12 , 1 - 0.16, 2 - 0.24, 3 - 0.32, 4 - ?, 5 - 0.05

What is 0.13?

300
The probability that one might grab an orange skittle out of a packet of skittles is 20%, if there are 24 skittles in a particular bag, this is the probability of finding at least 4 orange skittles.
What is .46 or 46%?
300
This is the probability that the on a multiple choice quiz with 4 options for each question, if you randomly select answers, your first correct answer will be on the 4th question.
What is 0.105 or 10.5%?
300

For any two random variables X and Y, if S = X + Y, what is μS ?

μX+μY

400

If a scenario is Binary, has a fixed # of trials, and the same probability of success for each trial, but each trial is not independent, we can check this other condition/rule instead. 

The 10% condition. If n is our sample size, and N is the population size, 

n<=0.10N

400
This is the expected number of tires that were under inflated when a mechanic checked the tire pressures on cars in one week, which resulted in the following probability distribution. x P(x) 0 0.3 1 0.25 2 0.25 3 0.15 4 0.05
What is 1.4 tires?
400
This is the probability that more than 7 out of 10 surgeries will be successful when the probability of having a successful surgery is 90%.
What is .93 or 93%?
400
The probability that a randomly selected Xbox fresh off the assembly line is defective is 9%. The probability that the first defective Xbox that comes off the assembly line is the 7th or 8th off the line is this.
What is .0976 or 9.76%?
400

As n gets larger, the Binomial Distribution approaches a Normal Curve, so we can use Normal Probability Calculations. What are the 2 parts of the Large Counts Condition?

np>=10 and n(1-p)>=10

500
The probability distribution that looks for the of the first time a success occurs, after a number of failures.
What is a geometric probability distribution?
500
This is the mean of the probability distribution below. It describes the number of televisions per household in a small town. x P(x) 0 0.01 1 0.17 2 0.28 3 0.54
What is 2.35 tvs?
500
When the probability of single television being defective is 14%, this is the probability that, out of 20 tvs, between 8 and 13 tvs inclusive are defective.
What is .018 or 1.8%?
500

The probability that Lamar Jackson of the Baltimore Ravens throws an incomplete pass is .32. What is the probability that of his first 12 pass attempts, he has 2 incompletions? (Assume independence)

0.14 or 14%

500

What is the Pythagorean Theorem of Statistics?

Variance of the Sum/Difference of Two Random Variables: 

If S = X + Y, then

σS2 = σX+Y2 = σX2 + σY2