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

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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). Select the correct answer from above options

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(i) W.k.t P(0) + P(1) + P(2) + P(3) = 1 ⇒ k + k/2 + k/4 + k/8 = 1 (8k + 4k + 2k + k)/8 = 1 15k = 8 Hence, k = 8/15 (ii) P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2) = k + k/2 + k/4 = 7k/4 = 7/4 x 8/15 = 14/15 And P(X > 2) = P(X = 3) = k/8 = 1/8 x 8/15 = 1/15 (iii) P(X ≤ 2) + P(X ≥ 2) = 14/15 + 1/15 = (14 + 1)/15 = 15/15 = 1

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