the joint pmf of precipitation X(mm) and runoff Y, (cubic meters per second,cms)(discretized for simplicity) due to typhoons at a given location is as shown in the table

1.)1. What is the probability that the next typhoon will bring a precipitation of 10mm or less and a runoff of less than 20cms?

2.After a typhoon, the rain gauge indicates a precipitation of 10mm. What is the probability that the runoff in this typhoon is 20 cms or more?

3.Are precipitation and runoff statistically independent? why?

4. Determine the correlation between precipitation and runoff. Interpret the result.

5.If the precipitation is 10 mm, what is the expected runof(cms) and what is the standard deviation?

	x=5	x=10	x=15
y=10	.05	.10	0.05
y=20	.10	.20	.25
y=30	0	0.15	0.10