we are given independent random variables X and Y distrubuted:  X ∼ poisson(θ) , Y ∼ poisson(2θ), and observations x = 3 and y = 5.  Show that the expression for the log-likehood function is given by:  l(θ)=[5ln(2)−ln(3!)−ln(5!)]+8lnθ−3θ.  Make a rough sketch of l(θ) with valeus from θ [0,10]. For which values of θ does l(θ) reach maximum.  Estimate the likelihood maximation estimate θ*  for the observed values x= 3 and y= 5

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