Stocks. Since the stock market began in 1872, stock prices have risen in about 73% of the years. Assuming that market performance is independent from year to year, what’s the probability that a) the...

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in
Let X denote number of years that it rises in n = 5 independent years, where
each has a probability p = 0.73
We denote this by:
X ∼ Binomial(n = 5, p = 0.73)
A P (X = 3), n = 3, p = 0.73
X ∼ Binomial(n = 3, p = 0.73)
P (X = 3) =
(
n
x
)
px(1 − p)n−x =
(3
3
)
(0.73)3(1 − 0.73)3−3 = 1 ∗ (0.73)3(0.27)0 =
0.389017 = 0.389017 ≈ 0.389
P (X = 3) = 0.389
Using excel function BinomDist(3,3,0.73,false) or TI-83/84 function
binompdf(3,0.73,3), exact answer is 0.389017
B P (X = 3), n = 5, p = 0.73
X ∼ Binomial(n = 5, p = 0.73)
P (X = 3) =
(
n
x
)
px(1 − p)n−x =
(5
3
)
(0.73)3(1 − 0.73)5−3 = 10 ∗ (0.73)3(0.27)2 =
0.283593 ≈ 0.283593 ≈ 0.284
P (X = 3) = 0.284
Using excel function BinomDist(3,5,0.73,false) or TI-83/84 function
binompdf(5,0.73,3), exact answer is...