Unit 6 Flashcards
Expected Value
UNIT 6: - “mean of a random variable” “weighted avg”
- expected outcomme, per trial, on avg, often sets of trials
- Sum of the products of probability and value, for each event in the same sample space
-> Multiply then add the products together
** “If I do ____ many times, on average I’ll ______ per trial
On calculator:
X in L1, P(X) in L2
Stat: Calc: 1-Var stats L1, L2
X mean is expected value, sigma is SD
* only on calculator
Discrete
UNIT 6: - Countable
- Isolated points on number line
*Quantitative
Continuous
UNIT 6: - Interval
- Range of values on number line
*Quantitative
Linear Combination
UNIT 6: Multiple means/SD’s that you will combine
3 Rules of Linear Combination
UNIT 6: 1. The average of both random variables is the sum of each of their average
–> Doesn’t have to be independent
–> M = Mx +/- My
2. The SD of both random variables is the square root of their variances (SD ^ 2)
–> HAS to be independent
–> sqrt. SDx^2 + SDy^2 (ALWAYS adding)
3. Any linear combinations of normally distributed variables is also normally distributed
BIF
UNIT 6: Binary
- Only TWO outcomes per trial, don’t have to be 50/50
Independent
- Trials are indpendent with constant probability of success
- Events aren’t changed: P(A) = P(A | B)
Fixed
- Fixed number (n) of trials
- N (population) > 10n (10 * sample)
- Use your brain (reasonably assume) if you have to
*ALL have to apply to be binomial
Binomial on a calculator
-UNIT 6: 2nd, disrt
- binompdf (n, p, k) -> PRECISELY k successes in n trials
OR
-binomcdf (n, p, k) -> AT MOST k successes in n trials
EXACTLY = bimompdf
AT MOST = bimoncdf DO NOT 1-
AT LEAST = 1 - bimoncdf (k - 1)
Binomial formula
UNIT 6: Don’t have to memorize!
k = # of successes
n = # of trials
P = probability of success
Mean & SD of binomial
UNIT 6: Mean = np
SD = sqrt np(1-p)
- Stop after # - mean/SD if not normal
Assume NORMALITY when SAMPLE (n) is big enough
UNIT 6: np ≥ 10
n (1-p) ≥ 10
**Memorize
Assume INDEPENDENCE when POPULATION (N) is big enough
UNIT 6: N ≥ 10n
**Memorize
