# RandomVariables_01

 Discrete random variable- A discrete random variable is a random variable that can take on only a finite or at most a countably infinite number of values Basic description of the probability mass function: function p such that and cumulative distribution function (cdf) Random variable a numeric outcome from a random problem support- The values a random variable can take on is the support of a variable The probability of k successes in a binomial distribution: Probability of all the variation of successful sequences in a binomial distribution Use of capital and lower case letters to describe random variables and their realizations capital= random variable possibilitieslowercase= realization (set of finite/interval of values) Continuous random variables has an interval or union of intervals as its support distribution- pattern and frequency we observe the random variable Formula for a geometric distribution Formula for a negative binomial distribution CDF theorum What do you get when you take the integral of a PDF? probability! Endpoints don't matter if you are finding probabilities for continuous functions T/F True How do you find probability from a PMF? sum of the range it has support for(discrete) How do you find probability for a PDF? Integrate over the range of interest Endpoints don't matter for a PMF T/F False What are values of the PDF often refered to as? relative liklihoods  (graph)  (graph) (graph) (graph) In a coin flip experiment to determine whether a coin is biased or not, what is an example of the following term: population all coins of this type In a coin flip experiment to determine whether a coin is biased or not, what is an example of the following term: parameter =p= P(coin lands on heads) In a coin flip experiment to determine whether a coin is biased or not, what is an example of the following term: sample Sequence of observed coin flips In a coin flip experiment to determine whether a coin is biased or not, what is an example of the following term: Statistic observed number of heads (y) or sample proportion of heads Support- values the random variables can take on The differences between CAPITAL and lowercase variables ex. X vs x little 'x' represents realization of the random variable big 'X' represents the actual random variable Support for a discrete random variable countable support Support for a continuous random variable interval (or union of intervals) for the support How can you identify a CDF of a random variable Y? Cumulative Distribution Function (cdf) of a random variable (Y) denoted as either:   or The cumulative probability up to and including the actualized value of (y) Graph the CDF and find CDF theorem: Frequency function The probability mass function of a discrete random variable: Probability density function (PDF) a continuous random variable is the function that satisfies:or Describe a PDF PDF is a visualization of the distribution of your random variable PMF/PDF theorem: For discrete random variables, the probabilities are the sum of the PMF over the range of interest and (end points do matter) T/F True For continuous random variables, the probabilities are the integrals of the PDF over the range of interest and (end points do matter) T/F FalseEnd points DO NOT matter Solving for probability for a discrete variable: (PMF or PDF? describe how to solve) PMF Solving for probability for a continuous variable: (PMF or PDF? describe how to solve) integrating factor= constant required to make an integral = 1 What are the values of the PDF often refered to as? "relative likelihoods" Does f(a) or f(b) have a higher liklihood? f(a) Formula for finding probability from a CDF: Formula for finding probability from a PDF: Formula for finding probability from a PMF: Expected value for a random variable Y: Expected Value (or Mean) of a RV Y , denoted as E(Y)= µY , is the average value of Y weighted by the probability distribution. Authorsaucyocelot ID362566 Card SetRandomVariables_01 DescriptionIntro to random variables Updated2023-12-10T05:55:41Z Show Answers