Prompt 2: The number of eggs laid on a tree leaf by an insect of a certain type is a Poisson random variable, XXX, with parameter ccc, where E(X)=cE(X)=cE, left parenthesis, X, right parenthesis, equals, c. However, such a random variable can only be observed if it is positive, since if it is 0, then we cannot know that such an insect was on the leaf. If we let YYY denote the observed number of eggs, then P(Y=i)=P(X=i∣X>0)P(Y=i)=P(X=i∣X>0)P, left parenthesis, Y, equals, i, right parenthesis, equals, P, left parenthesis, X, equals, i, vertical bar, X, is greater than, 0, right parenthesis, where XXX is Poisson with parameter ccc.
Find E(Y)E(Y)E, left parenthesis, Y, right parenthesis.
(Note 1: your answer will be a mathematical expression with ccc. When you type in your answer, the preview box will display what the mathematical expression looks like.
Note 2: Coursera uses the capital letter "E" to represent the mathematical constant "e" equivalent to approximately 2.72.)