5. It has been observed that the annual peak discharge O (in m3 s" ) for a given river can be described by Fuller's formula, as follows: 9=294[1+0.3In7, ) where , is the recurrence interval (i.e., return period) of the peak discharge of magnitude Q. (a) Derive the probability distribution function F=F(Q) from Fuller's formula. (b) What is the probability that the 700 m' s flood will be exceeded every single year in a 4 yr period? (c) What is the probability that the 700 m' s flood will be exceeded only once, namely at the end of this 4 yr period? In other words, what is the probability that this flood will not be exceeded during the first 3 yrs and then will be exceeded during the last year