Exercise #2 (35pt): The flood duration (in hour) recorded by a streamgauge station can be modeled...

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Exercise #2 (35pt): The flood duration (in hour) recorded by a streamgauge station can be modeled by a random variable X with the following Cumulative Distribution Function (CDF): Fx(x) = ax2 + 0.1x for x = [0,12] Q1 (5pt). Determine the constant a. Approach: 2pt Computation: 2pt Numerical result: 1pt Q2 (5pt). What is the probability that the flood duration is greater than 7h? Approach: 2pt Computation: 2pt Numerical result: 1pt Q3 (5pt). Determine the Probability Density Function (PDF) of X. Approach: 2pt Computation: 2pt Numerical result: 1pt Q4 (5pt). Calculate the mean of the flood duration. Approach: 2pt Computation: 2pt Numerical result: 1pt Q5 (5pt). Calculate the median of the flood duration. Approach: 2pt Computation: 2pt Numerical result: 1pt Q6 (5pt). Calculate the standard deviation of the flood duration. Approach: 2pt Computation: 2pt Numerical result: 1pt Q7 (5pt). If a current flood started three hours ago, what is the probability that it will be over within another hour? Approach: 2pt Computation: 2pt Numerical result: 1pt Exercise #2 (35pt): The flood duration (in hour) recorded by a streamgauge station can be modeled by a random variable X with the following Cumulative Distribution Function (CDF): Fx(x) = ax2 + 0.1x for x = [0,12] Q1 (5pt). Determine the constant a. Approach: 2pt Computation: 2pt Numerical result: 1pt Q2 (5pt). What is the probability that the flood duration is greater than 7h? Approach: 2pt Computation: 2pt Numerical result: 1pt Q3 (5pt). Determine the Probability Density Function (PDF) of X. Approach: 2pt Computation: 2pt Numerical result: 1pt Q4 (5pt). Calculate the mean of the flood duration. Approach: 2pt Computation: 2pt Numerical result: 1pt Q5 (5pt). Calculate the median of the flood duration. Approach: 2pt Computation: 2pt Numerical result: 1pt Q6 (5pt). Calculate the standard deviation of the flood duration. Approach: 2pt Computation: 2pt Numerical result: 1pt Q7 (5pt). If a current flood started three hours ago, what is the probability that it will be over within another hour? Approach: 2pt Computation: 2pt Numerical result: 1pt