Statistics and Probability Answers

For each of the following, find the constant c so that p(x) satisfies the condition of being a probability density function of a random variable X:
I. p(x) = c(2/3)^x, x ∈ N
II. p(x) = cx, x ∈ {1,2,3,4,5,6}

For each of the following, find the constant c so that p(x) satisfies the condition of being a probability density function of a random variable of x:

I. p(x) = c(2/3)^x, x E N

II. p(x) = cx, x E {1,2,3,4,5,6}


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1. Consider a game with two players, Jim and Annie. Annie has a red die and Jim has a white die. They roll their dice and note the number on the upper face. Annie wins if her score is higher than Jim's (note that Jim wins if the scores are the same). Investigate the game when they can roll the dice more than twice, but not necessarily the same number of times. (difficult )

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Answer

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