題組內容

1.(20%) For a random variable x defined on the real number line, denote its probability density function and cumulative distribution function as f(x) and Fx(a), respectively. By definition, 62032c826e8eb.jpg
and the expectation of any function g(x) can be derived as62032caada650.jpg62032cca48b02.jpg

(a) (10%) Define Hx(η) = 62032cfc0087e.jpgda. Prove that 62032d465f2e4.jpg(Hint: you can consider to change the order of integration.) ifn-x＜0