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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: (refer to picture) (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) Are X and Y statistically dependent? Substantiate your answer. (c) Determine and plot the marginal PMF of runoff. (d) Determine the correlation coefficient between X and Y.

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: (refer to picture) (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) Are X and Y statistically dependent? Substantiate your answer. (c) Determine and plot the marginal PMF of runoff. (d) Determine the correlation coefficient between X and Y.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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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: (refer to picture)

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

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

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

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
Transcribed Image 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
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