4.1: Uniform and Binomial Distributions Flashcards
Discrete Random Variables - a random variable that can take on…
At most a countable number of possible values (possibly infinite).
Continuous Random Variable - a random variable that…
Has only continuous values (uncountable and related to integers).
Cannot count, but can measure volume.
Probability Distributions can be viewed in two ways:
- Probability Function - a function that specifies the probability that…
- The Cumulative Distribution Function (cdf) - a function giving the…
The random variable takes on a specific value P(X = x).
Probability that a random variable is less than or equal to a specified value.
For a discrete random variable, the shorthand notation for the probability function (sometimes referred to as the “probability mass function”) is…
For continuous random variables, the probability function is denoted … and called…
p(x) = P(X = x)
f(x), the probability density function (pdf), or just the density.
Suppose that the possible outcomes are the integers (whole numbers) 1–8, inclusive, and the probability that the random variable takes on any of these possible values is the same for all outcomes, that is, it is..?
Uniform
Bernoulli Random Variable - a random variable having the outcomes…
0 (failure) and 1 (success).
Binomial Distribution is when the following criteria’s are met:
B
I
N
S
Binary Outcomes (1 or 0)
Independent Trials
“N” # of Trials
Same p (probability) per Trial
CALCULATINNG BINOMIAL PROBABILITY DISTRIBUTIONS:
P(x) = nCx * p^x * (1 - p)^n-x
Where nCx is the Combination formula (order does not matter)
Binomial Probability Distribution Mean is calculated as?
Mean for population:
μ = n*p
Binomial Probability Distribution Variance is calculated as?
Σ^2 = V(X) = n*p(1-p)
Binomial Probability Distribution Std.Dev. (sq.root of Var.) is calculated as?
σ = √np(1-p)
