Expectation of a Binomial Experiment: Suppose you conduct a random experiment that has a binomial probability distribution. Suppose the probability that outcome C occurs on any one repetition is 0.4. Let P(x) be the probability that outcome C occurs x times in five repetitions. a. Calculate P(x) for each value of x in the domain. b. Find the mathematically expected value of x. (Hint: The value if C occurs x times is x.) c. Show that the mathematically expected value of x is equal to 0.4 (the probability C occurs on one repetition) times 5 (the total number of repetitions). d. If the probability that C occurs on any one repetition is b and the probability that C does not occur on one repetition is a = 1 b, prove that in five trials, the expected value of x is 5b. e. From what you have observed in this problem, make a conjecture about the mathematically expected value of x in n repetitions, if the probability that C occurs on any one repetition is b. f. If you plant 100 seeds, each of which has a probability of 0.71 of germinating, how many seeds would you expect to germinate?

Notes for 308 Specially Designed Instruction (SDI) and Related Services: SDI - Additions, deletions, changes and/or modifications that will assist a student in being successful with or within… o The curriculum o The learning environment o Their IEP goals Related Services – additional things a student requires to be successful that must be delivered by a specific provider o Transportation, speech and language, OT, PT, etc Educational Placement Explanation of the extent, if any, to which the student will NOT participate with students without disabilities in regular education class Explanation of the extent, if any, to which the student will NOT participate with students without disabilities