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problemset11

# problemset11 - STAT/MA 416 Problem Set 11 Name 1a Variance...

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STAT/MA 416 September 16, 2011 Problem Set 11 Name: 1a. Variance of an Indicator. Suppose event A occurs with probability p , and X is an indicator for A , i.e., X = 1 if A occurs, or X = 0 otherwise. We already know E ( X ) = p . Find Var( X ). 1b. Butterflies. Alice, Bob, and Charlotte are looking for butterflies. 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 catch altogether. Find the variance of X . 1

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2. Appetizers. At a restaurant that sells appetizers: 8% of the appetizers cost \$1 each, 20% of the appetizers cost \$2 each, 32% of the appetizers cost \$3 each, 40% of the appetizers cost \$4 each.
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