Statistics Flashcards
What is the formula for calculating probability of events a and b occurring together where event a depends on event b
Probability of event A and Event B occurring together = probability of event A given event B, (the probability that event A will happen if assumed that event B has already happened, refers to event B as guaranteed so does not represent event B’s probability) multiplied by the probability of event B
What is the formula for calculating the probability of events A and B occurring together where events are independent
The probability that event A and event B will occur together when independent is probability that event A will occur multiplied by the probability that event B will occur. If events are independent the probability that event A will occur when given event B is equal to the probability that event A will occur when given event B bc the occurrence of event B does not affect the likelihood that event A will occur.
How do you determine probability of choosing an option when they are not replaced, (makes probability of the option that you choose dependent on the option that you last chose)
Subtract the amount taken from the most specific subcategory it fits into to get the new subcategory total then add up the quantities for all of the subcategories to get the new total. These will allow you to find the probability for the next options.
How do you find the probability that event A will occur given event B
The probability of Event A occuring given Event B = the probability of event A and B occuring together divided by the probability of event B occuring.
Explain random variable contingency tables
When looking at how often a random option is represented in an outcome a value can be assigned to represent the frequency that the option occurs in each outcome. When crating a table for this the x collomn looks at te frequency of the option, (does not represent probability of option in outcome just represents count of option in outcome so can be greater then 1). The probability colomn in turn does not represent probaiblity of getting option in outcome but rather represents the probability of the outcome occuring out of the total number of outcomes, so should not = 0 even if option count is 0 bc refers to likelihood of outcome not probaiblity of option in outcome.
How do you find probaiblity of an event?
Multiply the probabilities of getting outcome specified in each subcategory by each other to get total probability of event, (do using and formula with each options proability x the probability of the option that came before it) - different option arrangments= different outcomes so can not just rep one arrangment must rep each possible order.
What does biased mean?
Biased does not mean dependent just means that options are not all equally likely to occur.
What is the formula for the expected value of a random variable and what does this refer to
Formula for calculating expected value of a random variable = E(x) = (frequency of x1 multiplied by probability of x1) + (frequency of x2 multiplied by probability of x2)… + (frequency of xn multiplied by probability of xn)
The expected value of a random variable refers to the average ammount of variable, (based on each option) we would get over time
How do you find the average number of times an event has to occur in order to get a specific outcome
1 = nP(event) we set to 1 bc we are looking for average number of times
