(Solved): The joint probability distribution of precipitation \( X \) (inches) and runoff \( Y(\mathrm{cfs ...

The joint probability distribution of precipitation \( X \) (inches) and runoff \( Y(\mathrm{cfs}) \) (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 in. and a runoff of more than 20 cfs? Enter your answer to three decimal places. The answer is: b. Referring to the runoff distribution, the rain gauge after a storm indicates a precipitation of 2 in. What is the probability that the runoff in this storm is 20 cfs or more? Enter your answer to three decimal places. The answer is: c. Referring to the runoff distribution, what is the expected value of \( X \) ? Enter your answer to two decimal places. d. Referring to the runoff distribution, what is the standard deviation of \( X \) ? Enter your answer to two decimal places. The answer is: e. Referring to the runoff distribution, what is the covariance of \( X \) and \( Y \) ? Enter your answer to two decimal places. The answer is: f. Referring to the runoff distribution, what is the correlation of \( X \) and \( Y \) ? Enter your answer to four decimal places. The answer is: