Question

puterized stock trading program recommends stocks that show a profit with probability 0.60. The computer is programmed to recommend one stock per trading day number of stocks recommended by the computer program until the first profitable stock. Is the distribution of XGeometric? Explain. Answer: Yes (b) Let W number of profitable stocks recommended by the computer program over the next 200 trading days. Is the distribution of W Geometric? Explain. Answer: No (c) Find the probability of at least three profitable stock recommendations over the next five trading days. Answer: 0.683 (d) Find the expected number of profitable stock recommendations over the next 200 trading days. Answer: 120 (4.5.6)
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Answer #1

a)as trail continues till we receive our first success and trail success is independent and fixed from trail to trail therefore it is a geometric distribution

b)

here as number of trails are fixed therefore it is a binomial distribution and not geometric distribution

c)

P(3 or more profitable recommendations)=P(X=3)+P(X=4)+P(X=5)

=5C3(0.6)3*(0.4)2+5C4(0.6)4*(0.4)1+5C5(0.6)5*(0.4)0=0.3456+0.2592+0.0778 =0.683

d)

expected number =np=200*0.6 =120

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