Question

Suppose that the daily fluctuation in the price of a company stock is a random variable X that is uniformly distributed on the interval -1 to 1. Suppose that a broker observes 243 trading days. What is the probability that the daily fluctuation is less than 0.5?

Answer 1

The probability that the daily fluctuation is less than 0.5 is 0.75.

Step-by-step explanation:

To find the probability that the daily fluctuation is less than 0.5, we need to calculate the proportion of the interval -1 to 1 that is less than 0.5.

Since the random variable X is uniformly distributed on the interval -1 to 1, the probability is equal to the length of the subinterval -1 to 0.5 divided by the length of the entire interval -1 to 1.

Length of subinterval -1 to 0.5 = 0.5 - (-1) = 1.5

Length of entire interval -1 to 1 = 1 - (-1) = 2

Probability = (Length of subinterval -1 to 0.5) / (Length of entire interval -1 to 1) = 1.5 / 2 = 0.75

Therefore, the probability that the daily fluctuation is less than 0.5 is 0.75.