Probabilty Flashcards
Probability as Odds
p/1-p
P(A or B)
P(A)+P(B)-p(AB)
Joint Probability
P(AB)=P(A|B)*P(B)
Independent Probability
P(AB)=P(A)*P(B)
Total Probability Rule
P(AB)= P(A|B)P(B)+P(A|Bc)P(Bc)
Covariance
Probabilitydeviation1deviation2
Corr
(Cov.ab)/(sa*sb)=p
Porfolio VARIATION
(s.a)^2(w.a)^2+(s.b)^2(w.b)^2+2w.aw.bs.zs.b*p.ab
Binomial Random Variable
[n!/(n-x)!x!]/p.x*(1-p)^n-x
Tracking Error
R.p-R.b
Normal Distribution Charesteristics and Confidence Intervals
Completely described by mean+variance Kurtosis=3 1.65s-90% 1.96s-95% 2.58s-99%
Safety-First Ratio
R.p-R.l/s.p
R.l=Target Return
Sampling Error
Difference between sample statistic and true population mean
Central Limit Theorem
For any population size, as the size of the sample increases, the closer the sample statistic gets to the population statistic and gets closer to the normal distribution
Standard Error
s/sqrt(n)
Point Estimate
Mean+/-(StandardError*Confidence Interval)
Use T-statistic when:
Unknown Variance
Use Z Statistic when:
Known Variance
No Test Available when:
small sample size, nonnormal distribution, unknown variance
Type I Error
Rejecting true Null Hypothesis
Probability equal to the confidence interval
Type II Error
Fail to reject false null hypothesis
Z-statitstic
x`-u/[s/sqrt(n)]
T statistic formula
x`-u/[s/sqrt(n)]
Difference in Means Test
Tests wether two normal independent populations have equal means
DMT is independent
Mean Differences Test
Tests difference between means of 2 DEPENDENT samples
Chi-squared test
Tests wether the variance of a normal poopulation is x, two-tailed test
F Test
Tests wether the variance of 2 normal populations is equal
Populations can be two different sizes
Parametric/Non-parametric tests
Parametric tests rely on parameters and distributions charesteristics
