Question

Flood level analysis. Researchers have discovered that the maximum flood level (in millions of cubic feet per second) over a 4-year period for the Susquehanna River at Harrisburg, Pennsylvania,follows approximately a gamma distribution with α=3 and β=0.07 (Journal of Quality Technology, Jan.1986). Find the mean and variance of the maximum flood level over a 4-year period for the SusquehannaRiver. (Mean is 0.21 and variance is 0.0147)

Answer 1

The mean of the maximum flood level for the Susquehanna River with α=3 and β=0.07 is 0.21 million cubic feet per second, and the variance is 0.0147 million cubic feet per second squared.

Step-by-step explanation:

The student's question pertains to a gamma distribution and the task is to find the mean and variance of the maximum flood level for the Susquehanna River at Harrisburg, Pennsylvania using the given parameters α (alpha) and β (beta). The gamma distribution parameters provided are α=3 and β=0.07.

The mean of a gamma distribution is calculated using the formula αβ, which in this case gives us 3 * 0.07 = 0.21 million cubic feet per second. Similarly, the variance of a gamma distribution is obtained using the formula αβ², resulting in 3 * (0.07)² = 0.0147 million cubic feet per second squared. These results provide insights into the typical flood levels and their variability over the four years observed.