Suppose that the number of plants of a particular type found in a rectangular sampling region (called a quadrat by ecologists) in a certain geographic area is an rv X with pmf Is E(X) finite? Justify your answer (this is another distribution that statisticians would call heavy-tailed).

Answer : Step 1 : Suppose that the number of plants of a particular type found in a rectangular sampling region (called a quadrat by ecologists) in a certain geographic area is an rv X with pmf. Yes.E (X) is finite. The explanation is E(X) = xp(x = n) x=1 E(X) = x c x3 x=1 c E(X) = x2 x=1 E(X) = c 12,, ut it is a well-known result from the theory of infinite series that x=1 x 1 x2 < x=1 So E(X) is finite.