Between 1896—when the Dow Jones index was created— and 2012, the index rose in 65% of the years. Based on this information, and
assuming a binomial distribution, what do you think is the probability that the stock market will rise a) next year? b) the year after next? c) in four of the next five years? d) in none of the next five years? e) For this situation (modeling Dow Jones index), what assumption of the binomial distribution might not be valid? Are the years independent?
1 answer:
Answer:
a) P(x) = 0.67
b) P(y) = 0.67
c) P(x=4) = 0.3325
d) P( x = 0 ) = 0.0039
e) The dependence of stock market fluctuations on market sentiment compromises the assumption of independence utilized in the Binomial distribution; the years themselves are independent.
Step-by-step explanation:
A) The likelihood of the stock market rising in the next year is equal to P(x) = 0.67 assuming the following year is X.
B) The likelihood of an increase in the stock market the following year is P(y) = 0.67 due to independence from prior years
C) The likelihood of a rise in the stock market for four out of the next five years is P(x=4) = 0.3325
D) The likelihood of no increases occurring in the next five years is P(x = 0) = 0.0039
E) The link between market behavior and sentiment breaches independence in the Binomial distribution while the years remain independent.
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