Mosquitoes will bite times per second on average in the forest. You only know that 0 1. As you arrive to the forest, it takes x_1 =5+N seconds till the first bite, when N=8.Write down the value of N clearly and use that numerical value in the calculations below.

(a) Model the unknown parameter as a random variable and write a prior distribution f() which fits the problem statement above to it.

(b) Assume that the time Xi between consecutive bites follows the exponential distribution X_i Exp() with density function f(x | ) = e^(x) when x 0 and = 0 otherwise. Based on the prior and observation X_1 = x_1, calculate the posterior distribution for (you can ignore the normalization constant).

(c) Calculate the maximum a posteriori estimate (posterior mode)