1. Suppose that ladybugs are distributed randomly and uniformly on the leaves of apple trees at a rate of 2 per tree. In an orchard of 100 trees, 58 contained no ladybugs, and 42 contained one or more ladybugs. What is the maximum likelihood estimate of A? Hints: There are two different distributions involved in this question, and you will need to use the Invariance Property. A) 0.42 B) 0.58 0.545 D) 4.060 2. A continuous random variable, Y, has probability density function (pdf): f(y; 0) = (0 + 1)y , for 0 -1; 0, otherwise Suppose that we observe data: Vi yz ..., )n based on n independent random variables Y1, Yz, .Yn from the above distribution, what is the maximum likelihood estimate of 0? -n A) 8 = En log( vi) 1 B) 0 = y C) 8 = 1 Etz log (vi) D)