Consider a random sample of n observations X, Xn from the distribution with pdf given by...

 

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Consider a random sample of n observations X₁, Xn from the distribution with pdf given by f(x) = √O I 2√ exp{-√x}, > 0, with parameter 0 > 0. • First show that this is a density function by showing that it integrates to one. . Find the expected value E(X;). • Find the method of moments (MOM) estimator for • Find the maximum likelihood estimator (MLE) for and denote it by MOM. and denote it by MLE- Consider a random sample of n observations X₁, Xn from the distribution with pdf given by f(x) = √O I 2√ exp{-√x}, > 0, with parameter 0 > 0. • First show that this is a density function by showing that it integrates to one. . Find the expected value E(X;). • Find the method of moments (MOM) estimator for • Find the maximum likelihood estimator (MLE) for and denote it by MOM. and denote it by MLE-