An number cube a fair die is rolled 3 times For each roll we are interested in whether the roll comes up even or odd An outcome

Question

An number cube a fair die is rolled 3 times For each roll we are interested in whether the roll comes up even or odd An outcome is represented by a string of the sort oee meaning an odd number on the first roll an even number on the second roll and an even number on the third roll For each outcome let be the random variable counting the number of even rolls in each outcome For example if the outcome is oeo then N oeo 1 Suppose that the random variable x is defined in terms of as follows X 4N 2N 2 The values of x are given in the table below Outcome eoo ooo eee eeo ooe eoe oeo oee Value of X 0 Calculate the probabilities P X x of the probability distribution of x First fill in the first row with the values of x Then fill in the appropriate probabilities in the second row Value X of X 2 8 2 0 2 0 2 P X x 0 3 X 6

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