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

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0.4 Let: P(X = 0) = m P(X = 1) = k. Now, P(X = 3) = 2k xi pi pixi 0 m 0 1 k k 2 0.3 0.6 3 2k 6k Mean = \sum\nolimits_{}^{} pixi 0 + k + 0 . 6 + 6k = 1 . 3 \Rightarrow 7k = 1 . 3 - 0 . 6 \Rightarrow k = 0 . $\frac{7}{7}$ = 0 . 1 We know that the sum of probabilities in a probability distribution is always 1. $\therefore$ P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) = 1 \Rightarrow m + 0 . 1 + 0 . 3 + 0 . 2 = 1 \Rightarrow m + 0 . 6 = 1 \Rightarrow m = 0 . 4

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