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Conditional Probability P(AjB) = P(A;B)=P(B) { Probability of A, given that B occurred. Conditional Probability is Probability P(AjB) is a probability function for any xed B. Any theorem that holds for probability also holds for conditional probability.
Sample standard deviation for frequency table: = s n [ ∑ ( f • x 2 ) ] − [ ∑ ( f • x ) ] 2. n ( n − 1) Sample z-score: z = x − x s. Population z-score: z. −μ = x. σ. Interquartile Range: (IQR) = Q 3 − Q 1.
Question, E[XY ]: I toss a coin 3 times. X represents the number of heads in the first two tosses, and Y represents the number of heads in the last two tosses. Find E[XY ]. Solution: Let’s list all the possible outcomes (left) and the corresponding value of XY (right): HHH THH TTH.
Expected Value (aka mean, expectation, or average) can be thought of as the \weighted average" of the possible outcomes of our random variable. Mathematically, if x1;x2;x3;::: are all of the possible values that X can take, the expected value of X can be calculated as follows: E(X) = P xiP(X = xi) i.
This cheat sheet integrates a variety of topics in probability the-ory and statistics. It is based on literature [1,6,3] and in-class material from courses of the statistics department at the Univer-sity of California in Berkeley but also in uenced by other sources [4,5]. If you nd errors or have suggestions for further topics, I
Basic Probability Formulas. Complementary events: The complement of event A is everything not in A. Complementary events are mutually exclusive events and together make up the sample space. The probability of the sample space is one. Independent events: The occurrence of any one of the events does not affect the probabilities of the occurrences ...
Steps to Solve a Word Problem: Identify the events in the problem. In terms of these events, write down the probability that is being asked for in the problem. For each probability (number) in the problem, write down what its mathematical expression is, e.g., (A); P (Bc); P (A j B); etc.