Expected Value and Binomial Probabilities

There are two possible outcomes.

The probability of a success, p, is constant.

There are a fixed number of trials.

There are a fixed number of events.

The trials are independent.

the number of successes in a fixed number of trials

the number of failures in a fixed number of trials

the total number of trials

the probability of success in each trial

number of trials

number of parameters

number of successes

number of variables

the number of trials in the experiment

the expected value of the random variable

the probability of success for a single trial

the standard deviation of the random variable

probability of a failure

probability of a success

population size

population standard deviation

the factorial of a non-negative integer n

the product of a non-negative integer n

the sum of a non-negative integer n

the square of a non-negative integer n

mode

population mean

population median

range

Their distributions are approximately symmetric.

Trials must be fixed.

Events musts be independent.

The probability of success must be 0.50

$0.00

-$1.00

$1.00

$3.00