A random variable X takes the values 0, 1, 2, 3 and its mean is 1.3 . If P(X=3) = 2P(X=1) and P(X=2) = 0.3 , then P(X=0) is

Step-by-step solution

Let P(X=1) = p and P(X=0) = q . Given P(X=3) = 2P(X=1) = 2p and P(X=2) = 0.3 . The sum of all probabilities is 1 : P(X=0) + P(X=1) + P(X=2) + P(X=3) = 1 q + p + 0.3 + 2p = 1 q + 3p = 0.7 The mean of the random variable is given as 1.3 : x_i P(x_i) = 1.3 0(q) + 1(p) + 2(0.3) + 3(2p) = 1.3 p + 0.6 + 6p = 1.3 7p = 0.7 p = 0.1 Substituting the value of p in the first equation: q + 3(0.1) = 0.7 q = 0.4 Thus, P(X=0) = 0.4 . Answer: 0.4