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

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

Let's denote P(X = 1) as 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 = 1) = 1/4 and P(X = 0) = 3/4.

Now we can calculate the expected value E(X):

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

So, the expected value E(X) is 1/4.