6 Random Variables Flashcards
Given a probability distribution (a row of values and a row of probabilities), how do you calculate the mean?
Multiply down, add across. Multiply each value by its probability and add them all.
Given a probability distribution (a row of values and a row of probabilities), how do you calculate the standard deviation?
Subtract each value from the mean and square it. Then times it by the probability of that value (row 2). Then add these all up and take the square root.
How do you find an expected value or the expected amount of something?
This is just another word for mean. So use one of the formulas from the formula sheet.
How do you find a probability if all you are given is a mean and s.d.?
It’s almost definitely a normal curve. Sketch a curve for yourself and use normal cdf. If you have more than one set of means, you might need to add or subtract them first and make a new curve. Make sure you square the s.d.’s before adding them.
When should you add something to a standard deviation? Or when should you add standard deviations?
NEVER. When combining, square each s.d. first, add them all and then square root at the end.
How do you find a probability if all you are given is a chance of success and a little other information?
Almost definitely use binomial or geometric formulas/calculator functions
How do you find a mean and standard deviation if you are given a percent in the problem?
Almost definitely use the formulas in the binomial (np) or the geometric (1/p) section of the formula sheet.
When sampling without replacement, how big of a sample can I take and still have independent events?
Find 10% of the population size. Also, if the population is large you can just assume that your sample isn’t too big (but you might need to say that if prompted).
How do you interpret a standard deviation in this chapter?
Same way as always: The (variable in context) typically differs from the mean by (s.d.) units.
How do I know when to use geometpdf instead of binompdf?
When you are trying to find the probability that the first success is on the nth try. If you don’t have a set number of trials, you won’t be able to use binompdf anyway.
When would I want to do 1 minus a probability?
1 minus a probability always finds the opposite probability. Most common is if you want to find P(x > 5) using binom or geomet, you have to use cdf to get the probability of everything less and then subtract it from one. Remember: cdf includes the number you type, so make sure you don’t cut off a number that you need.
What does binomcdf(12, 0.2, 3) find?
P(x<=3) in a binomial setting with 12 trials and a 20% chance of success. This is the same as P(0) + P(1) + P(2) + P(3). It is also the same as P(x<4).
What does geometcdf(0.2, 3) find?
P(x<=3) in a geometric setting with a 20% chance of success. This is the same as P(1) + P(2) + P(3). It is also the same as P(x<4). So what is the probability that the first success was on the 1st, 2nd, or 3rd try?
What is the difference between a discrete and a continuous variable?
Continuous variables can take on an infinite number of values (like the length of your foot) but discrete variables can only be certain values (like shoe size). Note: discrete variables don’t have to only be integers.
What is the shape of a binomial distribution?
For a small number of trials it is unknown but once you have enough trials that the large counts condition is met (n*p and n(1-p) are both bigger than 10) it will be approximately normal.
