Example. Price Changes of a stock You buy a stock that is traded in a price that

Question

Example. Price Changes of a stock You buy a stock that is traded in a price that is rounded to the nearest dollar amount. In any given time period thereafter let the random variable X be the price change, which could range between (-10 to +15 dollars) with equal probability, say. a) What are the chances (i.e., probability) that X will be positive? b) What is the expected value of X? c) What is the probability that X will be at most 12.5? d) What is the probability that X will be at most 12? e) What is the probability that X will be at least 13.3?

Explanation / Answer

X ~ U(-10 , 15)

a) P(X > 0) = (15 - 0) / (15 - (-10)) = 0.6

b) Expected value = (15 + (-10)) / 2 = 2.5

c) P(X < 12.5) = (12.5 - (-10)) / (15 - (-10)) = 0.9

d) P(X > 12) = (15 - 12) / (15 - (-10)) = 0.12

e) P(X > 13.3) = (15 - 13.3) / (15 - (-10)) = 0.068

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