Reading...
Play button
Play button
Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
20 Cards in this Set
- Front
- Back
|
68-95-99.7 Rule (Empirical Rule)
|
In a Normal model, 68% of values fall within one standard deviation of the mean, 95% of values fall within two standard deviations of the mean, and 99.7% of values fall within three standard deviations of the mean
|
|
|
Addition Rule for Expected Values of Random Variables
|
E(X plus or minus Y) = E(X) plus or mins E(Y)
|
|
|
Addition Rule for Variances of Random Variables
|
(Pythagorean Theorom of Statistics) If X and Y are independent:
Var(X+or-Y) = Var(X) and Var(Y), and Standard Deviation(X+or-Y)= the square root of Var(X)+Var(Y) |
|
|
Bernoulli trials
|
A sequence of trials are called Bernoulli trials if:
1) There are exactly two possible outcomes (usually denoted success and failure) 2) The probability of success is constant 3) The trials are independent |
|
|
Binomial probability model
|
Is appropriate for a random variable that counts the number of successes in a fixed number of Bernoulli trials
|
|
|
Continuous random variable
|
A random variable that can take any numeric value within a range of values. The range may be infinite or bounded at either or both ends
|
|
|
Discrete random variable
|
A random variable that can take one of a finite number of distinct outcomes
|
|
|
Expected value
|
The expected value of a random variable is its theoretical long-run average value, the center of its model. It is found by summing the products of variable values and probabilities
|
|
|
Geometric probability model
|
A model appropriate for a random variable that counts the number of Bernoulli trials until the first success
|
|
|
Normal model
|
The most famous continuous probability model, the Normal is used to model a wide variety of phenomena whose distributions are unimodal and symmetric. The Normal model is also used as an approximation to the Binomial model for large n, when np and nq are greater than or equal to 10, and is used as the model for distributions of sums and means under a wide variety of conditions
|
|
|
Normal percentile
|
A percentile corresponding to a z-score that gives the percentage of values in a standard Normal distribution found at that z-score or below
|
|
|
Parameter
|
A numerically valued attribute of a model
|
|
|
Poisson model
|
A discrete model often used to model the number of arrivals of events such as customers arriving in a queue or calls arriving in a call center
|
|
|
Probability density function (pdf)
|
A function F(x) that represents the probability distribution of a random variable X. The probability that X is an interval A is the area under the curve f(x) over A.
|
|
|
Probability model
|
A function that associates a probability, P, with each value of a discrete random variable, X, denoted P(X=x), or with any interval of values of a continuous random variable
|
|
|
Random variable
|
Assumes any of several different values as a result of some random event. Random variables are denoted as a capital letter, X.
|
|
|
Standard deviation of a random variable
|
Describes the spread in the model and is the square root of the variance
|
|
|
Standard Normal model or Standard Normal distribution
|
Come back to this
|
|
|
Uniform model
|
For a discrete uniform model over a set of n values, each value has a probability 1/n. For a continuous uniform random variable over an interval {a,b}, the probability that X lies in any subinterval within {a,b} is the same and is just equal to the length of the interval divided by the length of {a,b} which is b-a.
|
|
|
Variance
|
The variance of a random variable is the expected value of the squared deviations from the mean. Put in the equation later
|
