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Stochastic Exam 1
| Question | Answer |
|---|---|
| P(AuB) | P(A) + P(B) |
| P(A|B) | P(AB)/P(B) |
| Independent events | P(AB) = P(A)*P(B) One probability does not effect the other |
| Mutually exclusive (disjoint) | Events cannot happen at the same time |
| If A and B are two mutually exclusive events, P(AnB) | 0 |
| If A and B are two mutually exclusive events, P(AuB) | P(A)+P(B) |
| If A and B are two mutually exclusive events, P(AnB^c) | P(A) |
| If A and B are not mutually exclusive, P(AuB) | P(A)+P(B)-P(AnB) |
| If A and B are not mutually exclusive, P(AnB^c) | P(A)-P(AnB) |
| How to show independence | P(A|B) = P(A) P(AnB) = P(A)*P(B) |
| IF A and B are independent P(AuB) | P(A) + P(B) - P(AB) |
| Expected value of a continuous variable | Integral from negative infinity to infinity (or on the defined values of the function) of xf(x) dx |
| Expected value of a Bernoulli variable | P |
| Expected value of a binomial variable | n*p |
| Expected value of a uniform distribution | (a+b)/2 |
| The CDF is | the integral of the PDF |
| The PDF is | the derivative of the CDf |
| Geometric distribution | p(n) = (1-p)^n-1 *p |
| Bernoulli distribution | p(1) = p p(0) = 1-p |
| Uniform distribution | 0 if x < a 1/(b-a) if a<x<b 0 if x>b |
| Variance | Ex^2 + (Ex)^2 |
| Ex^2 | Integral from negative infinity to infinity (or the defined interval) of x^2*f(x) dx |
| Ex | Expected value |
| Standard deviation | Sqrt of variance |
Created by:
slpause
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