A bridge will be designed according to $100-$yr flood discharge with an economic life of $50$ years. The

mean discharge and standard deviation that are obtained from $70$ years annual maximum flows on the

nearby gauge station are $\frac{?}{\text{b}\text{a}\text{r}}(Q)=$ Table $1$ and $=15\frac{m^3}{s},$ respectively.

q mean $=253$

$($a$)$ Determine the magnitude of $100-$yr flow, $Q_{100yr},$ on this river using Log$-$Pearson III Distribution.

$($b$)$ Determine the return period of $300\frac{m^3}{s}$ using Extreme Value Distribution.

$($c$)$ Determine the risk of the bridge.

$($d$)$ Determine the probability that the design flood, $Q_{100-y},$ occurs less than twice during the life time of

the bridge.