(Question 2) Short Questions (45 pts) 2.A (20 pts) You running an experiment tha

Question

(Question 2) Short Questions (45 pts) 2.A (20 pts) You running an experiment that costs $50. There are four possible outcomes for the results from the experiment. outcome Symbol valuc Great S100 Good $50 Bad SO S73 The historical outcomes of 40 experiments are: 4321432143 214321432 234123412 234123412 (a) (Spts) Let X be the outcome from one experiment. Write down the PMF of X. (b) (Spts) Let X be the outcome from one experiment. Write down the CDF ofX (c) (10pts) As a researcher your goal is to keep running the experiment until you obtain a great results (i) How many times you will be running the experiment? (5pts (ii What is the net revenue from all your experiments? (Spts)

Explanation / Answer

a) & b)

c)

probability of great result is 0.225

number of experiments expected to get great outcome = 1/ 0.225 = 4.44444

total revenue expected in 40 experiments = 2200

50*11 + 75*10 + 100*9 = 2200

X frequency pmf cdf 1 10 0.25 0.25 2 11 0.275 0.525 3 10 0.25 0.775 4 9 0.225 1 40

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