题目
In regard to the chi-squared and F-distribution, each of the following is true EXCEPT which is false?
选项
A.Both the chi-squared and F-distribution are non-negative and positively skewed to the right
B.The square of variable with a student's t distribution with df = k has an F-distribution with 1 and k df.; that is,「huixue_img/importSubject/1564169386560983040.png」
C.The sum of two independent chi-squared variables, with respectively k1 and k2 degrees of freedom, is itself chi-squared with (k1+k2) degrees of freedom
D.The chi-squared distribution is approximated by the ratio of two independent F-distributions; i.e., 「huixue_img/importSubject/1564169386594537472.png」
答案
D
解析
The F-distribution is the distribution of the ratio of two independent chi-squared random variables; i.e.,「huixue_img/importSubject/1564169386628091904.png」. Note that the F-distribution has two degrees of freedom while the chi-squared distribution has only one degree of freedom (such that its mean is k and its variance is 2k).