Question

6. Let X1, X2, ..., Xn be a random sample of a random variable X from...

6. Let X1, X2, ..., Xn be a random sample of a random variable X from a distribution with density

f (x)  ( 1)x 0 ≤ x ≤ 1

where θ > -1. Obtain,

a) Method of Moments Estimator (MME) of parameter θ.
b) Maximum Likelihood Estimator (MLE) of parameter θ.
c) A random sample of size 5 yields data x1 = 0.92, x2 = 0.7, x3 = 0.65, x4 = 0.4 and x5 = 0.75. Compute ML Estimate of θ.

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