Since the move in prices is 2% per day in either direction, the value of the DJIA after day one in the up state will be 10,000 * 1.02 = 10,200. After one day in the down state, the value will be 10,000 * (1 - .02) = 9,800. After two days in the up-up state, the value will be 10,000 * (1.02)2= 10,404.
The probability of the up-up state occurring is (.67)2= .4489. The probability of up-down is (.67)(.33) = .2211.
k: Describe the continuous uniform distribution and calculate probabilities, given a uniform probability distribution.
Note:We're pretty confident that there is a typo in your study guide here. LOS 1.D.kactually says to calculate probabilities using the binomialdistribution, but we did that in LOS 1.D.h.Therefore, we will calculate probabilities using the uniform distribution here.
The continuous uniform distributionis defined over a range that spans between some lower limit "a" and some upper limit "b" which serve as the parameters of the distribution. Outcomes can only occur between a and b. Because the distribution is continuous, even if a < x < b, p(x) = 0. For a ≤ x1≤ x2≤ b,
P(X < a or X > b) = 0