61. LetI mage be a sequence of independent identically distributed continuous random variables. We say that a record occurs at time n ifI mage. That is,I mage is a record if it is larger than each of

. Show

(a) Image;

(b) Image;

(c) Image;

(d) Let Image. Show Image.

Hint: For

(b) and

(c) represent the number of records as the sum of indicator (that is, Bernoulli) random variables.