# The probability density function given below describes a probability distribution used to model scores on certain...

###### Question:

The probability density function given below describes a probability distribution used to model scores on certain exams/tests:

?(?)={(?+1)?? for 0≤?≤1, 0 otherwise. The parameter θ must be greater than 1.

a. Find E(X).

A random sample of 10 test-takers gives the following scores in proportions:

0.96 0.43 0.77 0.85 0.93 0.79 0.77 0.85 0.74 0.98

b. Using part a, find the method of moments estimator for θ using the first moment of X based on the data above.

c. Find the maximum likelihood estimator for θ based on the data above.

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