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A loaded 8-sided die is loaded so that the number 4 occurs 3/10 of the time...

A loaded 8-sided die is loaded so that the number 4 occurs 3/10 of the time while the other numbers occur with equal frequency. What is the expected value of this die?

Math   Statistics-And-Probability   
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Answer #1

Given that a loaded 8-sided die is loaded so that the number 4 occurs 3/10 of the time while the other numbers occur with equal frequency.

That is probability of getting 4 is 3/10=0.3

Therefore, the probability of getting any number is 0.1, since there are remaining 7 numbers which occur with equal frequency.

Let, X be the value on a die. The probability distribution of X is given by:

X=x 1 2 3 4 5 6 7 8

P(X=x) 0.1 0.1 0.1 0.3 0.1 0.1 0.1 0.1

The expected value of the die is:

Hence the expected value of the die is:

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