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I need all answers where the number is not already filled in please

A normal six-sided die has the following (discrete) probabilities: Number Probability 1 1/6 1/6 1/6 1/6 1/6 1/6 What is the eA six-sided die is rigged to have the following probabilities: Number Probability 0.05 0.09 0.09 0.06 0.04 0.67 What is the eA game played with the rigged six-sided die has the following payouts based on the number that appears on a single roll: Numb

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Answer #1

Here' the answer to the question for all 3 parts with all calculations in the table below. Highlighted are answers below. As per forum rules, solving the 1st question.

1.

The E(X) is basically the expected value of x, which is basically the p(x) weighted value of X and is 3.5

The Standard deviation is Stdev(x) is basically the square root of Variance(x) = sqrt ( E(x^2) - E(x)^2) as calculated below and is 1.708

The average of roll of numbers on the dice is 3.5 ( 1+2+3+4+5+6)/6 = 3.5

p(x) x^2 Ex^2) 1 15.16666667 Var(x) = E(x^2) - (E(x)^2) 2.91666666666667 Stdev(x) = sqrt(Var(x)) 1.707825128 E(x) 0.17 3.5000

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