f 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) isans.

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 0 and 1, and that P(X = 0) = 3P(X = 1), we can first find the probability P(X = 1).

We know that the sum of all probabilities in a probability distribution must equal 1. Therefore, we have:

P(X = 0) + P(X = 1) = 1

Substituting P(X = 0) = 3P(X = 1) into the equation, we get:

3P(X = 1) + P(X = 1) = 1 4P(X = 1) = 1 P(X = 1) = 1/4

Substituting P(X = 1) = 1/4 into P(X = 0) = 3P(X = 1), we find:

P(X = 0) = 3 * (1/4) = 3/4

Now we can calculate the expected value 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.