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19 Cards in this Set
- Front
- Back
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What is a random variable?
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A variable that takes on a numerical value determined by the outcome of a random experiment
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What is a discrete random variable?
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A random variable is discrete if it can take on no more that a countable number of values. Example: 1, 200, 50...etc.
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What is a continuous random variable?
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A random variable is continuous if it can take any value in an interval. Example: 1, 3.5, 0.6...etc.
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What is the probability distribution function?
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P(x)= P(X=x), for all values of x
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What are the properties of the probability distribution function?
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1) P(x)> or = 0 for any value of x
2) The individual properties sum to 1 |
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What is a random variable?
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A variable that takes on a numerical value determined by the outcome of a random experiment
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What is a discrete random variable?
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A random variable is discrete if it can take on no more that a countable number of values. Example: 1, 200, 50...etc.
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What is a continuous random variable?
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A random variable is continuous if it can take any value in an interval. Example: 1, 3.5, 0.6...etc.
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What is the probability distribution function?
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P(x)= P(X=x), for all values of x
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What are the properties of the probability distribution function?
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1) P(x)> or = 0 for any value of x
2) The individual properties sum to 1 |
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What is the cumulative probability function?
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F(x 0)= P(X < or = x 0)
The sums of the probabilities |
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What are the properties for the cumulative probability function?
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1) 0 <= F(x 0) <= 1 for every number x 0
2) If x 0 and x 1 are two numbers with x 0 < x 1, then F(x 0) <= F(x 1) |
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What is the expected value?
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E(X)= ΣxP(x) value*probability
the notation indicates that summation extends over all possible values x. Also denoted as μ |
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What is the variance of a DRV?
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σ(2)= E(X(2))-μ(2)
value squared*probability+value squared*probability-expected value squared |
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What is the standard deviation of a DRV?
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the square root of the variance
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What is the probability function for binomial distribution?
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P X(r)= nCr π r (1-π) n-r
n=trials π=probability |
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What is the expected value, variance, and standard deviation in a binomial distribution?
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E(X)=n*π
Var(X)=n*π(1-π) SD(X)=square root of var(X) |
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What is the Poisson distribution?
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It counts the number of times an event occurs in a fixed period of time
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What is the Poisson probability function, expected value and variance?
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P X(r)= e(-λ) λ r/r!
E(X)= λ Var(X)= λ |
