The probability distribution of a random variable X is given below:


i. Determine the value of k


ii. Determine P (X≤2) and P(X>2)


iii. Find P (X≤2) + P (X>2)

The key point to solve the problem:


If a probability distribution is given then as per its definition, Sum of probabilities associated with each value of a random variable of given distribution is equal to 1


i.e. ∑(pi) = 1


Given distribution is :


(i)


∴




∴ (i)


(ii) P(X>2) = P(X = 3) =


∴ P(X>2) =


P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2) = = …(ii)


(iii) ∴ P(X>2) + P(X≤ 2) =


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