Explanation:
The expected value of a random binomial variable given that and is determined as follows: . The variance of the random binomial variable is calculated as follows: .
(Book 2, Module 14.1, LO 14.a)
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Question 99
Suppose you are trying to estimate the expected return and variance for a 6-day period performance of the Standard and Poor's 500 Index. Assume that daily movements in the S&P 500 are binomial random variables. Based on historical data, there is a 63% probability that the S&P 500 Index will increase and a 37% probability that it will decrease. Assuming that daily movements in the S&P 500 are independent, what is the expected value and variance of the number of positive days in a 6-day period?
A
Expected return is 0.63 and variance is 0.26.
B
Expected return is 3.14 and variance is 0.68.
C
Expected return is 3.25 and variance is 1.21.
D
Expected return is 3.78 and variance is 1.40.
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