If the random variable X assumes the values 0 and 1 only and is such that P(X = 0) = 3P(X = 1), then the value of E(X) is ans. 1/4 2/3 none 1/3
Question
If the random variable X assumes the values 0 and 1 only and is such that P(X = 0) = 3P(X = 1), then the value of E(X) is ans. 1/4
2/3
none
1/3
Solution
The expected value E(X) of a random variable X is calculated as the sum of all possible values of X multiplied by their respective probabilities.
Given that X can take on the values of 0 and 1, and that P(X = 0) = 3P(X = 1), we can set up the following equations:
Let P(X = 1) = p, then P(X = 0) = 3p.
Since the sum of all probabilities must equal 1, we have:
p + 3p = 1 4p = 1 p = 1/4
Therefore, P(X = 0) = 3 * (1/4) = 3/4 and P(X = 1) = 1/4.
Now, we can calculate E(X):
E(X) = (0 * P(X = 0)) + (1 * P(X = 1)) = (0 * 3/4) + (1 * 1/4) = 0 + 1/4 = 1/4
So, the expected value E(X) is 1/4.
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