Discrete Random Variable And Independent Random Variables Notes

Bayes' Formula and Independent Events PDF 8 Discrete Random Variables PDF 9 Expectations of Discrete Random Variables PDF 10 Variance PDF 11 Binomial Random Variables, Repeated Trials and the so-called Modern Portfolio Theory PDF 12 Poisson Random Variables PDF 13 Poisson Processes PDF 14 More Discrete Random Variables PDF 15

Previously we learned the probability rules for working with events in general. Next, we will adopt the rules of probability in the context of discrete random variables. For a discrete random variable 92X92, in addition to the sum of all probabilities being equal to 1 The inequality matters 92PX92leq aPXltaPXa92 The complementary rule

The expectation of a nonnegative random variable Xis de ned as EX supfEZ Zis simple and Z Xg Note that EX 0 because we can always take Z 0. We can have EX 1for instance, for a discrete random variable Xwith PX k 1 kk 1, k 23. For an arbitrary random variable X, we write X X X where X maxfX0g X1 fX 0g is the

Discrete Random Variables Denition A subset S of the red line R is said to be discrete if for every whole number n there are only nitely many elements of S in the interval nn. 0 So a nite subset of R is discrete but so is the set of integers Z. Lecture 6 Discrete Random Variables and Probability Distributions

1.2 Discrete random variables Before we dene discrete random variables, we need some vocabulary. Denition 1.2.1. Given a set B, we say that the random variable X is B-valued if PX 2B 1. In words, X is B-valued if we know for a fact that X will never take a value outside of B. Denition 1.2.2. A random variable is said to be discrete

Random Variables. Random Variables! quot-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 Trials are independent

For example, the number of heads obtained after flipping a coin three times is a discrete random variable. The possible values of this variable are 0, 1, 2, or 3. Examples of a Discrete Random Variable. A very basic and fundamental example that comes to mind when talking about discrete random variables is the rolling of an unbiased standard die.

If range Rof discrete random variable Xhas kelements, Xhas a uniform distribution with pmf fx 1 k for each x2R The mode of discrete random variable Xis the value of Xwhere the pmf is a maxi-mum. The median is the smallest number msuch that PX m 05 and PX m 05 A random variable with two modes is bimodel, with two or more modes

Random Variables A dsicrete random variable RV is a function from a sample space to the real numbers. The mathematical notation for a random variable X on a sample space looks like this X !R A random variable denes some feature of the sample space that may be more interesting than the raw sample space outcomes.

Discrete Random Variables 3.4 Zoo of Discrete RVs Part I From 92Probability amp Statistics with Applications to Computingquot by Alex Tsun In this section, we'll de ne formally what it means for random variables to be independent. Then, for the rest of the chapter 3.4, 3.5, 3.6, we'll discuss commonly appearing random variables for which we