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;
23 Cards in this Set
- Front
- Back
|
A variable (typically represented by x) that has a single numerical value, determined by chance, for each outcome of a procedure.
|
A random variable
|
|
|
A description that gives the probability for each value of the random variable. It is often expressed in the format of a graph, table, or formula.
|
A probability distribution
|
|
|
This variable has either a finite number of values or a countable number of values, where "countable" refers to the fact that there might be infinitely many values, but they can be associated with a counting process, so that the number of values is 0 or 1 or 2 or 3 etc.
|
A discrete random variable
|
|
|
This variable has infinitely many values, and those values can be associated with measurements on a continuous scale without gaps or interruptions.
|
A continuous random variable.
|
|
|
What are the two requirements of a probability distribution?
|
1) ∑P(x) = 1 (except for small rounding errors)
2) 0 ≤ P(x) ≤ 1 |
|
|
What is the formula for the Mean of a probability distribution?
|
µ = ∑[x • P(x)]
|
|
|
What is the formula for the variance of a probability distribution?
|
σ² = ∑[(x - µ)² • P(x)]
|
|
|
What is the formula for standard deviation for a probability distribution?
|
σ = √σ² (variance)
|
|
|
The range rule of thumb for standard deviation states:
|
most values should lie within 2 standard deviation of the mean. It is unusual for a value to differ from the mean by more than 2 standard deviations.
|
|
|
What is the formula for the range rule of thumb for standard deviation?
|
maximum usual value = µ + 2σ
Minimum usual value = µ - 2σ |
|
|
How are probabilities used to determine if results are unusual?
|
results are unusually high if:
P(x or more successes ≤ 0.05) results are unusually low if: P(x or less successes ≤ 0.05) |
|
|
What is expected value?
|
The expected value represents the mean value of infinite outcomes.
|
|
|
What is the formula for expected value?
|
E = ∑[x • P(x)]
|
|
|
Expected value =
|
µ
|
|
|
What are the requirements of a binomial probability distribution?
|
1) A fixed number of trials.
2) The trials must be independent. 3) Outcomes must fit into two categories, (usually success and failure). 4) Probability of success is the same in all trials. |
|
|
What is the 5% rule?
|
If a sample size is no more than 5% of a population, then the selection can be treated as independent.
|
|
|
n denotes:
x denotes: p denotes: q denotes: P(x) denotes: |
-the fixed number of trials.
-a specific number of successes in n trials, (any number -between 0 and n) -the probability of success in one of the n trials. -the probability of failure in one of the n trials. -the probability of getting exactly x successes among the n trials. |
|
|
P(S) =
|
p, the probability of a success
|
|
|
P(F) =
|
q, the probability of a failure
|
|
|
P(F); q =
|
1 - p
|
|
|
What is the binomial probability formula?
|
P(x) = {n! / (n - x)!x! } • Pˣ • qⁿ⁻ˣ
where: n = number of trials x = number of successes among n trials p = probability of success in any one trial q = probability of failure in any one trial (q = 1 - p) |
|
|
What is the procedure for finding binomial probability with the TI-84?
|
2nd - Distr - binomial pdf (n, p, x) then hit enter
|
|
|
In the formulas for binomial distribution:
µ = σ² = σ = |
np
npq √(npq) |
