Discrete Random Variables
Found 11 free book(s)AP Statistics Chapter 6 Discrete, Binomial & Geometric ...
www.danshuster.com6.1: Discrete Random Variables Random Variable A random variable is a variable whose value is a numerical outcome of a random phenomenon. Discrete Random Variable A discrete random variable X has a countable number of possible values. Generally, these values are limited to integers (whole numbers). The probability distribution of X lists the ...
Lecture 6: Discrete Random Variables - CMU Statistics
www.stat.cmu.eduLecture 6: Discrete Random Variables 19 September 2005 1 Expectation The expectation of a random variable is its average value, with weights in the average given by the probability distribution E[X] = X x Pr(X = x)x If c is a constant, E[c] = c. If a and b are constants, E[aX +b] = aE[X]+b. If X ≥ Y, then E[X] ≥ E[Y] Now let’s think about ...
3 Discrete Random Variables and Probability Distributions
www.colorado.eduTwo Types of Random Variables A discrete random variable: Values constitute a finite or countably infinite set A continuous random variable: 1. Its set of possible values is the set of real numbers R, one interval, or a disjoint union of intervals on the real line (e.g., [0, 10] ∪ [20, 30]). 2.
CONDITIONAL PROBABILITY Discrete random variables ...
ctools.ece.utah.eduDiscrete random variables DEFINITIONS, FORMULAS (CONT.) TOOL: Using the Law of Total Probability and the axiom that probabilities of all outcomes in the sample space sum to unity, we can derive additional equations for conditional probability.
S1 Discrete random variables - PMT
pmt.physicsandmathstutor.comS1 Discrete random variables . PhysicsAndMathsTutor.com (e) Var(X) (3) (Total 10 marks) 14. A fairground game involves trying to hit a moving target with a gunshot. A round consists of up to 3 shots. Ten points are scored if a player hits the target, but the round is over if the player
Chapter 5: JOINT PROBABILITY DISTRIBUTIONS Part 1 ...
homepage.stat.uiowa.eduIn general, if Xand Yare two random variables, the probability distribution that de nes their si-multaneous behavior is called a joint probability distribution. Shown here as a table for two discrete random variables, which gives P(X= x;Y = y). x 1 2 3 1 0 1/6 1/6 y 2 1/6 0 1/6 3 1/6 1/6 0 Shown here as a graphic for two continuous ran-
Review of Probability Theory - Stanford University
cs229.stanford.edu2.6 Some common random variables Discrete random variables X˘Bernoulli(p) (where 0 p 1): one if a coin with heads probability pcomes up heads, zero otherwise. p(x) = ˆ p if p= 1 1 p if p= 0 X˘Binomial(n;p) (where 0 p 1): the number of heads in nindependent flips of a coin with heads probability p. p(x) = n x px(1 p)n x X˘Geometric(p ...
Lecture 4: Random Variables and Distributions
www.gs.washington.edu• Random Variables. Random Variables! "-1 0 1 A rv is any rule (i.e., function) that associates a number with each outcome in the sample space. Two Types of Random Variables •A discrete random variable has a countable number of possible values •A continuous random variable takes all values in an interval of numbers.
Discrete and Continuous Random Variables
ocw.mit.edu15.063 Summer 2003 44 Discrete Random Variables A probability distribution for a discrete r.v. X consists of: – Possible values x 1, x 2, . . . , x n – Corresponding probabilities p
1 Discrete-time Markov chains - Columbia University
www.columbia.edu1 Discrete-time Markov chains 1.1 Stochastic processes in discrete time A stochastic process in discrete time n2IN = f0;1;2;:::gis a sequence of random variables (rvs) X 0;X 1;X 2;:::denoted by X = fX n: n 0g(or just X = fX ng). We refer to the value X n as the state of the process at time n, with X 0 denoting the initial state. If the random
1 Acceptance-Rejection Method - Columbia
www.columbia.eduAcceptance-Rejection Algorithm for continuous random variables 1. Generate a rv Y distributed as G. 2. Generate U (independent from Y). 3. If U ≤ f(Y) cg(Y), then set X = Y (“accept”) ; otherwise go back to 1 (“reject”). Before we prove this and give examples, several things are noteworthy: • f(Y) and g(Y) are rvs, hence so is the ...