Question

6. In classes like Math 11 or Math 183, you often learn that the time an electronic device (e.g., cell phone, transistor) will last before breaking follows the exponential distribution. This statement sugar-coats the truth, because the chance that something fails should go up as it lasts longer, and the exponential distribution has the memorylessness property, which contradicts this intuition A better distribution to model the lifetime of electronics is: fy(y; α, β)-aßyß-1e-av', where y 0, α > 0, β > 0 Assuming Yi, ,y, are iid from this distribution, find the MIME for α assuming that β is fixed (known). Hint: To find the formula for E(Y), work the integral into a form that looks like a Gamma distribution. This is the hard part of the problem.

MME = Method of Moment Estimator

Answer 1