题目
Consider the following five random variables: A standard normal random variable; no parameters needed. A student's t distribution with 10 degrees of freedom; df = 10. A Bernoulli variable that characterizes the probability of default (PD), where PD = 4%; p= 0.040 A Poisson distribution that characterizes the frequency of operational losses during the day, where lambda = 5.0 A binomial variable that characterizes the number of defaults in a basket credit default swap (CDS) of 50 bonds, each with PD = 2%; n = 50,p = 2% Which of the above has, respectively, the lowest value and highest value as its variance among the set?
选项
A.Standard normal (lowest) and Bernoulli (highest)
B.Binomial (lowest) and Student's t (highest)
C.Bernoulli (lowest) and Poisson (highest)
D.Poisson (lowest) and Binomial (highest)
答案
C
解析
Bernoulli (lowest) and Poisson (highest) In order: Bernoulli has variance = p(1-p) = 4%×96 = 0.0384 Binomial has variance = p(1-p)n = 2%×98%×50 = 0.980 Standard normal has, by definition, mean = 0 and variance = 1.0 Student's t has variance = df/(df-2) = 10/8 = 1.25 Poisson has lambda = variance = mean = 5 伯努利试验（最低）和泊松分布（最高） 顺序由低到高为： 伯努利试验方差= p（1-p）= 4％×96 = 0.0384 二项分布方差= p（1-p）n = 2％×98％×50 = 0.980 标准正态分布平均值= 0，方差= 1.0 学生t分布方差= df /（df-2）= 10/8 = 1.25 泊松分布Lambda =方差=均值= 5