A coin is DAMAGED so that the probability of seeing HEADS is 0.25. Flip this coin 3 times and observe what happens. Lets use S (success) to denote heads and F (failure) to denote tails.

Q9. Calculate the POPULATION VARIANCE of X by using the general formula?

Q10. Calculate the POPULATION STANDARD DEVIATION of X?

In addition to the tree diagram for the probability distribution and general formulas for

the mean and standard deviation, there are special ways to efficiently get the answers

as below:

BINOMIAL PROBABILITY DISTRIBUTION FORMULA

Let p = probability of success for each trial

n = total number of trials

X = total number of successes observed

Then

State the special formula and calculate the answer.

P(X=x) = _____________________________________________________

P(0) =

P(1) =

P(2) =

P(3) =

m = _________________________________________________________

s² = ________________________________________________________

s = _________________________________________________________

Note: The above formulas are solely for the binomial probability distribution, a special type, but NOT USEFUL for other kinds of probability distribution derived from other NON-BINOMIAL random experiments.