题目
Let random variable W be distributed normally as N(0,10). What are, respectively, the following: 1)The fourth moment of ; and 2)The kurtosis of W?
选项
A.30.0 (4th moment) and zero (kurtosis)
B.100.0 and 3.0
C.300.0 and zero
D.300.0 and 3.0
答案
D
解析
N(0,10) signifies a normal distribution with mean = 0, variance = 10;and, by definition, skew=0 and kurtosis=3.0「huixue_img/importSubject/1564169387429203968.png」.In this case, therefore, 「huixue_img/importSubject/1564169387475341312.png」.The fourth moment「huixue_img/importSubject/1564169387508895744.png」.By the way, the fourth moment about the mean,「huixue_img/importSubject/1564169387550838784.png」, is therefore also equal to 300,since the mean is zero.