The joint probability distribution of precipitation X (inches) and runoff Y(cfs) (discretized here for simplicity) due to storms in the Lower Kaskaskia Valley is as follows: (a) What is the...


The joint probability distribution of precipitation X (inches) and runoff Y(cfs) (discretized here for simplicity) due to storms in the Lower Kaskaskia Valley is as follows:




(a) What is the probability that the next storm will bring a precipitation of 2 or more inches and a runoff of more than 20 cfs?


(b) After a storm, a precipitation of 2 inches is measured. What is the probability that the runoff in this storm is 20 cfs or more?


(c) Are X and Y statistically dependent? Substantiate your answer.


(d) Determine and plot the marginal PMF of runoff.


(e) Determine the correlation coefficient between X and Y.


X=1 X=2 X=3<br>Y=1<br>0.05<br>0.15<br>Y=2<br>0.1<br>0.25<br>0.25<br>Y=3<br>0.1<br>0.1<br>

Extracted text: X=1 X=2 X=3 Y=1 0.05 0.15 Y=2 0.1 0.25 0.25 Y=3 0.1 0.1

Jun 08, 2022
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