Question

7, If the number of event occurrences is Poisson distributed, successive occurrences is exponentially distributed. In certain locations in Texas, sudden heavy rainfall may produce sudden floods, called flash floods, because of the land surface geometry and other geographical factors. If a flood (event) occurs in any one day, we may the day a "flood day.' The flood days average 10 per year based on data over many years past i. Find the probability that 8 flood days will occur next year. ) = P( ii. What is the average time (in year) between consecutive flood days? iii. If a flood occurred today, find the probability that the third flood day from now, n counting today's, will occur within 4 months. PC ) =

Answer 1

Let X denote the number of flood days next year

P(X = x) = , x = 0,1,2,3,....

e-10 + 10%

i) The required probability = P(X = 8)

= = 0.1126

e-10 * 108

ii) The average time between consecutive flood days = 1/10 = 0.1 year

VULL DU: The average time for = 0.1X3 =0.3 years... three flood days third the ..... Let t denote the time ton ...blood day ham now. ..... Welt) = obeats too The requires probability - =P(t cu months) - Pltez tears 13 - tep =0.671