Expected Value and Binomial Probabilities

Assumptions for the binomial model is

• 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

Another term for our expected value (μ) is

• mode

• population mean

• population median

• range

What is the Expected Value?

(a)  

Which of the following is false about binomial probabilities?

• Their distributions are approximately symmetric.

• Trials must be fixed.

• Events musts be independent.

• The probability of success must be 0.50

Suppose you pay $1.00 to roll a fair die with the understanding you will get $3.00 back rolling a 4 or a 2, and nothing otherwise. What is the expected amount you win?

• $0.00

• -$1.00

• $1.00

• $3.00