Ams 310 Survey Of Probability And Statistics Worksheet - Midterm Exam I - Stony Brook University Page 7
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11(5). If a share of stock is allowed to go up and down 50 cent each day and if the probability
of going up or down is 50 percent. Let the stock starts from 20 dollars per share,
after 40 days, what is the probability that the stock price is below 15 dollars or
above 25 dollars?
The stock will have the price
if the number of ups is
Solution:
15
S
25
between
. The stock daily gain is a Bernoulli probability and for 40
15
x
25
days,
25
25
40
40
P (15
x
25) =
B(x; 20, 0.5) =
0.5
x
=15
=15
The probability of stock price beyond this range is
25
40
40
P (x < 15) + P (x > 25) = 1
P (15
x
25) = 1
0.5
x
=15
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