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Probability density function "a function of a continuous random variable, whose integral (an area or a generalization of area.)
across an interval gives the probability that the value of the variable lies within the same interval."
P(a ≤ x ≤ b) = ∫ f (x) dx
conditional expectation, conditional expected value, or conditional mean
The [] of a random variable is the expected value of the random variable itself, computed with respect to its [] probability distribution.
In probability theory, the [...] of a random variable is its expected value given that a certain set of "conditions" is known to occur. ... Y], is a function of the random variable Y and hence is itself a random variable.
?? "When you want to find out what are the chances that one specific thing will happen. Example: if I ask for a raise, what are the chances that my boss will leap over the desk and strangle me?"
Bayes Rule What are the chances I like BAYESwatch, given that I once had dreadlocks?
describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if cancer is related to age, then, using [ ] a person's age can be used to more accurately assess the probability that they have cancer, compared to the assessment of the probability of cancer made without knowledge of the person's age.
Geometric distribution Discrete. Generates the probability of X-trials required until the first occurrence is obtained.
Sampling from a series of independent trials of which have a binary outcome. How many licks does it take to get to the tootsie roll center of a tootsie pop? how many math classes did I have to take to get to the first one I liked, named:
Poisson distribution Discrete. Expresses the probability of a given number of events occurring in a fixed interval of time and/or space. Requirements: these events occur with a known average rate and are independent.
What are the chances I'll draw three aces in the first 10 cards I draw? Fishy gambling math. :)
(3 heads in a row, I think)
What are the chances that this patch of ground contains 3 buried bullets?
If this patch of ground contains 3 buried bullets, what are the chances that's a fluke?
binomial distribution "The probability that an unordered outcome will occur "a frequency distribution of the possible number of successful outcomes in a given number of trials in each of which there is the same probability of success."
1: The number of observations n is fixed. 2: Each observation is independent. 3: binary outcomes ("success" or "failure").
Binomial = two outcomes
"probability distribution function" minute 5:43 in class
Bias estimator
probability of events A and B
probability of events A or B
probability of event A given event B occured
conditional probability probability of event A given event B occured
probability density function equation
Sigma notation
Sigma is probability? because it's iterative
Conditional probability equation
population mean symbol The M is crying because it's mean
Expectation value Conditional expectation
expected value of random variable X given Y
Poisson distribution equation (needs work) "x" is sometimes "k". They mean "number of observed events"
"a" or lambda: expected number of events
lambda: "average rate of success for a given interval."
geometric distribution equation #2. Make sense?
binomial distribution equation **
bernoulli equation
Combination notation **
probability vs statistics Probability deals with predicting the likelihood of future events, while statistics involves the analysis of the frequency of past events.
Probability is primarily a theoretical branch of mathematics, which studies the consequences of mathematical definitions. Statistics is primarily an applied branch of mathematics, which tries to make sense of observations in the real world.
Difference between weak and strong law The difference between the weak and strong laws of large numbers is similar. The weak law guarantees that the probability that the sample mean is far away from the true average goes to zero. The strong law, on the other hand, guarantees that events of the form "the sample mean is far away from the true average" eventually stop happening.
Bernoulli distribution In probability theory and statistics
the probability distribution of any single experiment that asks a yes-no question; the question results in a boolean-valued outcome, a single bit of information whose value is success/yes/true/one with probability p and failure/no/false/zero with probability q. It can be used to represent a coin toss where 1 and 0 would represent "head" and "tail" (or vice versa), respectively. In particular, unfair coins would have {\displaystyle p\neq 0.5} p\neq 0.5.
probability distribution In probability theory and statistics, a probability distribution is a mathematical function that, stated in simple terms, can be thought of as providing the probabilities of occurrence of different possible outcomes in an experiment.
Bayes forumula / notation probability something happened given that something else happened
CHI squared when you have two categorical variables from a single population. It is used to determine whether there is a significant association between the two variables.
For example, in an election survey, voters might be classified by gender (male or female) and voting preference (Democrat, Republican, or Independent). We could use a chi-square test for independence to determine whether gender is related to voting preference.
Rule of 3 In statistical analysis, the rule of three states that if a certain event did not occur in a sample with n subjects, the interval from 0 to 3/n is a 95% confidence interval for the rate of occurrences in the population. When n is greater than 30, this is a good approximation to results from more sensitive tests.
