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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*probabilityexpected 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 (1π) nr
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(1π) 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 