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# Midterm Review Prob

### Review of main ideas from units 1, 2, 3, and 4 in Probability and Statistics.

continuous variable quantitative data with no gaps between values
discrete variable quantitative data with gaps between consecutive values
frequency table a table that describes the number of times a value or interval of values occurs in a data set, can be turned into a probability distribution by adding the total frequencies and dividing each frequency by the total
outlier an extreme value that is far from the rest of the values in a data set; in a data set, any number less than the lower fence or greater than the upper fence
upper fence Upper fence = Q3 + (1.5 * IQR)
lower fence Lower fence = Q1 – (1.5 * IQR)
interquartile range (IQR) the range of the middle half of the data set, IQR = Q3 - Q1
linear transformation adding or subtracting (or multiplying or dividing) the same nonzero quantity to each value in a data set, we use the table in our notes to help calculate
mean the sum of the data values divided by the number of data values; it is also called the average, in probability distributions this is the expected value
median the middle value when the data are ordered. If there is an even number of data values, the median is the average of the two middle values, this can also be called Q2
quartiles the three values that separate an ordered data set into four equal parts, between each quartile you have 25% of the data
fundamental counting principle to find the total combinations when you choose 1 item from seperate groups multiply the number of items in each group. IE You have 3 shirts, 5 pants, and 2 jackets 3*5*2 = total outfits
complementary events two events such that one must occur, but both cannot occur at the same time, this relates to binomial distributions, you either have a success or failure with opposite probabilities
dependent events two events related in such a way that knowing about one event's occurrence has an effect on the outcome of the other event, this is found in two way tables when we limit ourselves to 1 column or when we do not replace a chosen item.
experimental probability as the number of independent trials in an experiment increases, it becomes more likely that the experimental probability of an event gets close to the theoretical probability of the same event, should equal to theoretical probability in fair experiments
independent events two events related in such a way that knowing about the occurrence of one event has no effect on the probability of the other event
law of large numbers as the number of independent trials in an experiment increases, it becomes more likely that the experimental probability of an event gets close to the theoretical probability of the same event
mutually exclusive events events that have no outcomes in common IE king and ace are mutually exclusive, even and odd are mutually exclusive
overlapping events events having one or more outcomes in common
mutually exclusive events formula P(A or B) = P(A) + P(B) P(A and B) = 0 due to no overlap
overlapping events formula P(A or B) = P(A) + P(B) - P(A and B) P(A and B) = only the overlap
permutation formula, nPr n! / (n - r)! Or use Desmos.
combination formula, nCr n! / (n - r)!r! Or use Desmos.
permutation The number of different ways that a group of objects can be arranged. Order matters
combination The number of different ways to select a number of objects from a group. Order does not matter
P(A U B) P(A) + P(B) - P(A n B)
P(A|B) The probability of A given than B has already happened. We use this when looking only at a specific row/column in a table.
When do we use nPr? When we are looking for possible permutations of items where order matters. Like if we want to choose 1st, 2nd, and 3rd place. Once you come in 1st you can't be in 2nd, so order matters.
When do we use nCr? When we are looking for possible combinations of items where order does not matter. Like if we want to choose 5 grand prize winners. They all win equally, so order doesn't matter.
Independent Events Formula for event A and B with a total of N A/N * B/N We don't need to change the number we divide by. You can do this for as many events as you need to.
Dependent Events Formula for event A and B with a total of N A/N * B/(N -1) We need to change the number we divide by to show that the first even already happened. Just keep decreasing N for each additional event.
Fundamental Counting Principle Formula if event A has m outcomes and event B has n outcomes, then event A followed by event B has m×n outcomes
68-95-99.7 Rule Describes the percentage of data within 1, 2, and 3 standard deviations of the mean.
Raw Score an original data value, our random variable value
Percentile rank The percentage of data that fall below a particular value Example: if you are in the 95 percentile, you are above 95% of the rest of the data
How would you find P(x = 1 and 4) from a probability distribution? You can't, in a probability distribution table each separate row or column is mutually exclusive.
Binomial Distribution Probability Formula p(success)^#success * p(# failures)^#failure * n!/s!f! For all successes p(success)^#trials For all failures p(failure)^#trials For example: success = .3 fail = .7 2 success and 2 failure .3^2 * .7^2 * 4!/(2!2!)
Created by: sgulbis