Exercise 1. The maximum height # of the annual flood of a river is carefully observed, because a flood greater than 6meters would be catastrophic. We model the distribution of the random variable H by a Rayleigh law whose probability density is given by f(x) = -e & if x > 0 and 0 otherwise, where a is an unknown parameter. Over an 8-year period, the following (assumed to be independent) flood heights in meters were observed: 2.1;2.8; 1.7;0.9; 1.8;2.5;2.2;2.9. 1. Check that f defined a probability density function. 2. Give the MLE of the parameter a. 3. Give the cumulative distribution function of H. 4. Compute the probability of a disaster. 5. Give the probability to not have a flood during 100 years