Let y 1 , y 2 , , y n be a random sample of size n from the pdf f Y (y ) 2y 2 , 0 y Find a formula for the method of moments estimate for Compare the values of the method of moments estimate and the maximum likelihood estimate if a random sample of size 5 consists of the numbers 17, 92, 46, 39, and...

Let y 1 , y 2 , . . . , y n be a random sample

Question:

Let y₁, y₂, . . . , y_n be a random sample of size n from the pdf f_Y(y; θ) = 2y/θ², 0 ≤ y ≤ θ. Find a formula for the method of moments estimate for θ. Compare the values of the method of moments estimate and the maximum likelihood estimate if a random sample of size 5 consists of the numbers 17, 92, 46, 39, and 56