*84. Let be independent and identically distributed nonnegative continuous random variables having density function Image. We say that a record occurs at time n if is larger than each of the previous values . (A record automatically occurs at time 1.) If a record occurs at time n, then is called a record value. In other words, a record occurs whenever a new high is reached, and that new high is called the record value. LetI mage denote the number of record values that are less than or equal to t.

Characterize the processI mage when

(a) f is an arbitrary continuous density function.

(b) .

Hint: Finish the following sentence: There will be a record whose value is between t and if the first that is greater than t lies between …