Alice, Bob, and Charlotte are looking for but-terflies. They look in three separate parts of a field, so that their probabilities of success do not affect each other.
• Alice finds 1 butterfly with probability 17%, and otherwise does not find one.
• Bob finds 1 butterfly with probability 25%, and otherwise does not find one.
• Charlotte finds 1 butterfly with probability 45%, and otherwise does not find one.
Let X be the number of butterflies that they find altogether.
Write X as the sum of three indicator random variables, X1, X2, X3 that indicate whether Alice, Bob, Charlotte (respectively) found a butterfly. Then X = X1 + X2 + X3. Find the expected value of X by finding the expected value of the sum of the indicator random variables.