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You have three six-face fair dice: red, blue and white. The three dice are rolle

ID: 3151536 • Letter: Y

Question

You have three six-face fair dice: red, blue and white. The three dice are rolled together and repeatedly, and the observed numbers of dots in each die are recorded for each trial. Let X be defined as the random variable representing the trial time at which you observe an identical number of dots in all three dice for the first time. For example, if the first trial gives (R3, B4, W6) (i.e., red die has 3 dots; blue die has 5, and white die has 6) and the second trial yields (R4, B4, W4), then X=2, and so on. What is the probability mass function for X? What is expected value of X, E[X]

Explanation / Answer

the first question is correct for my criteria

expected value of X

the expected value you will find with the pmf that you have in a) multiply by X in each probability

you just need to sum all the multiplication and you will have the expected value

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