ch 6 random variable & probability distribution

p( x ≤ k )

( n ) k n-k ( 0 ) (p) (1-p) + ... binomcdf (n, p, k)

p(x < k)

( n ) k n-k ( 0 ) (p) (1-p) + ... ( n ) k n-k ( k-1 ) (p) (1-p) binomcdf (n, p, k-1)

p( x = k )

( n ) k n-k ( k ) (p) (1-p) bincompdf (n, p, k)

p( x ≥ k)

( n ) k n-k ( k ) (p) (1-p) + ... ( n ) k n-k ( n ) (p) (1-p) 1-binomcdf (n, p, k-1)

p(x > k)

( n ) k n-k ( k+1 ) (p) (1-p) +... ( n ) k n-k ( n ) (p) (1-p) 1-bincomcdf (n, p, k)

mean/expected value in context

If you were to repeat a random sampling process many, many times, the mean value would be about µx in the long run

standard deviation value in context

On avg, a randomly selected process will differ from the mean by about SD(x)

discrete random variable example

Which of the following is a discrete random variable? I. The average height of a randomly selected group of boys. II. The annual number of sweepstakes winners from New York City. III. The number of presidential elections in the 20th century. The annual number of sweepstakes winners* is an integer value and it results from a random process; so it is a discrete random variable.* The average height of a group of boys could be a non-integer, so it is not a discrete variable. And the number of presidential elections in the 20th century is an integer, but it does not vary and it does not result from a random process; so it is not a random variable. *II only*

geometric expected value

µ = 1/p