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### 19 Cards in this Set

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