问题如下:
If the probability that a portfolio outperforms its benchmark in any quarter is 0.75, the probability that the portfolio outperforms its benchmark in three or fewer quarters over the course of a year is closest to:
选项:
A.0.26
B.0.42
C.0.68
解释:
C is correct.
The probability that the performance is at or below the expectation is calculated by finding F(3) = p(3) + p(2) + p(1) + p(0) using the formula:
p(3)=(4−3)!3!4!0.753(1−0.75)4−3=(24/6)(0.42)(0.25)=0.42
p(2)=(4−2)!2!4!0.752(1−0.75)4−2=(24/4)(0.56)(0.06)=0.20
p(1)=(4−3)!1!4!0.751(1−0.75)4−1=(24/6)(0.75)(0.02)=0.06
p(0)=(4−0)!0!4!0.750(1−0.75)4−0=(24/24)(1)(0.004)=0.004
Therefore
F(3) = p(3) + p(2) + p(1) + p(0)= 0.42 + 0.20 + 0.06 + 0.004= 0.684 or approximately 68 percent.
请问计算器要如何操作呢?