Week 6 Discrete and Continuous Random Variables Binomial and Geometric Random VariablesBinomial and Geometric Random Variables

Question 1

Random Variable

Answer 1

A variable that takes on a numerical value that is a result of some chance
process. a variable whose value is unknown or a function that assigns values to each of an experiment’s outcomes. A random variable can be either discrete (having specific values) or continuous (any value in a continuous range).

Question 2

Probability Distribution

Answer 2

Provides the possible values of the random variable and their
probabilities. Describes all the possible values and likelihoods that a random variable can take within a given range

Question 3

Discrete Random Variable

Answer 3

A random variable whose value comes from a finite list of
potential outcomes. One that can only take on a finite or countably infinite number of values, often representing counts or outcomes that can be listed individually, like the number of heads in coin flips.

Question 4

Mean of a Random Variable also known as Expected Value E(x) or μ

Answer 4

the weighted average of all possible values, with weights being the probabilities of those values.

Question 5

Continuous Random Variable

Answer 5

A random variable whose value may come from an infinite set
of possibilities (despite potentially having upper and lower bounds or other restrictions). a random variable that can take on a continuum of values. In other words, a random variable is said to be continuous if it assumes a value that falls between a particular interval. Continuous random variables are used to denote measurements such as height, weight, time, etc.

Question 6

Binomial Setting

Answer 6

Performing several independent trials of the same chance process and record the number of times a particular outcome occurs. describes a probability experiment with a fixed number of independent trials, each having only two possible outcomes (success or failure), and a constant probability of success for each trial

Question 7

Binomial Random Variable

Answer 7

A random variable which measures the number of times a binomial trial is successful. Counts how often a particular event occurs in a fixed number of tries or trials For a variable to be a binomial random variable, ALL of the following conditions must be met: There are a fixed number of trials (a fixed sample size). On each trial, the event of interest either occurs or does not. The probability of occurrence (or not) is the same on each trial.

Question 8

Binomial Coefficient

Answer 8

The number of ways of arranging k successes among n observations. denoted as “n choose k” or (n k), represents the number of ways to select k items from a set of n items, without regard to order, calculated as n! / (k! * (n-k)!). the number of ways of picking unordered outcomes from possibilities, also known as a combination or combinatorial number.

Question 9

Geometric Setting

Answer 9

Performing independent trials of the same chance process and recording
the number of trials until a particular outcome occurs. scenario where you’re interested in the number of independent trials needed to achieve the first success, where each trial has only two possible outcomes (success or failure) with a constant probability of success.

Question 10

Geometric Random Variable

Answer 10

A random variable which measures how many trials it takes to
achieve a particular outcome. counts the number of independent trials needed to achieve the first success in a series of Bernoulli trials, where each trial has only two possible outcomes (success or failure) with a constant probability of success. tells you the number of experiments that were performed before obtaining a sucess. This random variable can thus take values of 1, 2, 3, …