Probability Part 2

Discrete/Continous

Refers to whenever the variable is countable steps or without gap like distance.

Expected Value

E(X): Refers to an average result (expected result given probability) over many, many trails

Probability Distribution

Mean of Expected Value (𝜇x)

Refers to the long-run average value of the variable after many, many trials of the random process.

Multiple all values to the frequency

Standard Deviation of Expected Value (σx)

Refers to how much the values of the random variable typically vary from the mean in many, many trials of the random process

stdv(1-mean)value²+….

Variance

Measure of how spread out a data set is, calculated by finding the average of the squared deviations from the mean

Geometric Distribution

Probability function that measures how many trials it takes to achieve the first success

Binomial Distribution

Probability function that calculates the chances of getting a certain number of desired results

Cumulative Distribution Function

Calculates the probability that a random variable will take on a value less than or equal to a specific value "x"

Probability Density Function

Calculates the probability of a continuous random variable taking on a specific value within a given range

B inary

I ndependent

N umber of sets

S ame probability

Condition for a binomial or geometric distribution

Large counts condition

Sampling distribution of sample proportions to be approximately normal, the counts of successes and failures in a sample must both be large enough, typically at least 10.

"np" (number of successes) and "n(1-p)" (number of failures) should be greater than or equal to 10

np

Mean of a Binomial Random Variable

√np(1−p)

Standard Deviation of Binomial Random

1/p

Mean of Geometric Random

(√1-p)/p

Standard Deviation of Geometric Random

NP>10

N(1-P)>10

Law of Large Count