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