Recall that for a random variable to be a binomial randomvariable, you must have an experiment which meets the followingthree criteria:
1: There are exactly two outcomes for each trial.
2: There are a fixed number (n) of trials.
3: The trials are independent, and there is a fixed probability ofsuccess (p) and failure (q) for each trial.
For each of the two situations described below, please indicateif the variable X (as defined in each situation) can be considereda binomial random variable. If you think that X is a binomialvariable, please explain how the situation specifically meets eachof the three criteria, and identify the values of n andp. If you think X cannot be considered a binomialvariable, please indicate which of the three criteria is/are notmet (indicate all that apply), and provide a brief explanation foryour choice(s). Hint: X can be considered a binomial randomvariable in only one of the two situations below, but I am nottelling you which one, obviously.
Situation 1: A fair coin is tossed over and over again. Let X =the number of tosses until the third TAILS appears.
Situation 2: A box contains 10 marbles: 4 are red, 3 are white,and 3 are blue. A marble is randomly selected, returned to the box,then another marble is randomly selected. Let X = the number of redmarbles selected in the two consecutive trials.
