Question:
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).
Solution:
(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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