A random sampleY1 , Y 2 , ⋯,Yn is drawn from a distribution whose probability density function is given by: f (Y ) = βe − βY , Y  0 & β > 0 a). Obtain the maximum likelihood estimator (MLE) of β. b)....

A random sampleY1 , Y 2 , ⋯,Yn is drawn from a distribution whose probability density function is given by: f (Y ) = βe − βY , Y  0 & β > 0

a). Obtain the maximum likelihood estimator (MLE) of β.

 b). Given that ∑ n Y i = 25 , ∑n Yi 2 = 50 , n = 50 calculate the maximum likelihood i =1 i =1 estimate of β.

( c). Using the same data as in part (b), test the null hypothesis that β =1against the alternative hypothesis that β ≠1at 5% level of significance