Question

Problem 5 (20 points) The joint probability mass function of precipitation depth X (mm) at a rain gauge station and flow Y (m/s) of a nearby river is as follows: X=25 li Y=2 0.05 Y=4 0.11 Y=6 a. Confirm that this is a valid joint PMF (using its properties) b. Find the marginal PMFs of X and Y. c. If the rain gauge indicates a precipitation of 50mm, what is the probability that the flow exceeds 4 m3/s?

Answer 1

./7 * Please give X=25 Y= 2 0.05 4 d.ll = 6 0 Total 0.16 positive de X-50 0.12 0.3 0.12 54 mandy X= 75 total O o.) .si 0.2 .32 -30 1 1 (marginalot) a for a valies joint pof Total Probability should be on. & p(x,y) = 7 - As we get from table total prob- is one. So this in the valid joint prof. marignal of margicala P(X=25) = 16 /P (7-2) = 017 P(X= 50 - 54|P(7-4)= 5) P(x-75) - .30 1PCY=6)= 32

Pood that flow exeeds 493/S, when gage indicates precipation of 50mm = P(Y=6/X= 50) = 0.12 Ctoom giver table)