The storm runoff X (in cubic meters per second, cms) from a subdivision can be modeled by a random variable with the following probability density function: for0 Sx S6 =0 otherwise a. Determine the constant c and sketch the PDF. b. The runoff is carried by a pipe with a capacity of 4cms. Overflow will occur with the runoff exceeds the pipe capacity. If overflow occurs after a storm, what is the probability that the runoff in this storm is less than 5cms? C. An engineer considers replacing the current pipe by a larger pipe having a larger capacity of 5cms. Suppose there is a probability of 60% that the replacement would be completed prior to the next storm. What is the probability of overflow in the next storm? The storm runoff X (in cubic meters per second, cms) from a subdivision can be modeled by a random variable with the following probability density function: for0 Sx S6 =0 otherwise a. Determine the constant c and sketch the PDF. b. The runoff is carried by a pipe with a capacity of 4cms. Overflow will occur with the runoff exceeds the pipe capacity. If overflow occurs after a storm, what is the probability that the runoff in this storm is less than 5cms? C. An engineer considers replacing the current pipe by a larger pipe having a larger capacity of 5cms. Suppose there is a probability of 60% that the replacement would be completed prior to the next storm. What is the probability of overflow in the next storm?