SOLUTION: A discrete random variable X can assume the values 10 and 20 only. If E (X) = 16,determine the probability distribution of X .

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Question 977825: A discrete random variable X can assume the values 10 and 20 only. If E (X) = 16,determine the probability distribution of X .
Answer by solver91311(24713) About Me  (Show Source):
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Assume that there are a total of samples comprising this distribution, of which have a value of 10. Then since the only other value is 20, samples must have a value of 20.

The probability of a 10 value is then and the probability of a 20 value is

Then, the expected value for the distribution is the probability of a 10 value times 10 and the probability of a 20 values times 20, thus:



Solve for in terms of a fraction of , and the fraction will be , the probability of a 10 value.

John

My calculator said it, I believe it, that settles it