The expected value of a "strange die" that has the values {2,3,4,6,7,8} the expected value is  ... _________________________________________________________ in case you ask, a "normal" die is this, giving values 1 to 6.    Numerical

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Peter does a lot of commuting by cycle.  Occasionally he gets a puncture while out riding (and very occasionally two).  Peter wants to determine the expected value for the number of punctures on a ride, so that he can determine how many puncture repair patches he should purchase to get him through 100 rides. Let x be the number of punctures on a given ride. The probability of getting one puncture is p(1) = 0.08 The probability of getting two punctures is p(2) = 0.01 The probability of getting zero punctures is 1 - p(1)-p(2) Find the expected value for the number of punctures for a given ride and multiply this by 100 and then round to the nearest integer to determine how many patches Peter should purchase.  Type your answer below.

You own a portfolio with the following expected returns given the various states of the economy. What is the overall portfolio expected return? State of Economy Probability of State of Economy Rate of Return if State Occurs Boom .11 .110 Normal .68 .045 Bust .21 −.045

In Ventura Bay, 20% of families have no children, 20% have one child, 40% have two children, 20% have three children, and 0% have four or more children. You randomly select 30 families from Ventura Bay to take part in a study regarding sugar intake. Assume all children from those 30 families participate in the study. What is the expected value of the total number of children (sample sum) you expect to be in the study? 

Suppose I am playing a game.  I bet $2.  There is a 40% chance that I win my $2 back plus another $1 There is a 20% chance that I win $2 back (break even) There is a 40% chance that I lose my $2 bet.  Using the box model and R, calculate the EV of the sample sum of playing this game 10 times.

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