Question

Suppose that earthquakes occur in a certain region on the average ln(2) per year.

a) Let X denote the # of earthquakes that occur in a year; making proper assumptions, write the pmf Px(x) of X and compute the probability of no earthquake occurs in one year

b) one investigator records the # of years Y until first year found in which no earthquake occurred. making use of (a), write pmf Py(Y) of Y and then find E(Y) and Var(Y)

Answer 1

8.@ x folloos poisson distribution where mean, a= ena =>P(x=x)= Œ^. -'.plx=x): ēme Unz)" aize 2. 2! *. Plx=0); nz)° 0.5) 2.01 .5] O Y follows geometric odistribution uhore (9) y-1 :. P(Y=y): (0.5)0 ; y-i,2,3, - - ELY)= !/þ = %3D VarlY)= (1-)2-0.5 O.52 12 %3D