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Let a random variable X take values 0, 1, 2, 3 with P(X = 0) = P(X = 1) = p, P(X = 2) = P(X = 3) and E(X2) = 2E(X). Then the value of 8p - 1 is :
(1) 2
Let P(X = 2) = P(X = 3) = k.
Total probability: 2p + 2k = 1 ...(i)
E(X) = 0 p + 1 p + 2k + 3k = p + 5k
E(X2) = 0 p + 1 p + 4k + 9k = p + 13k
E(X2) = 2E(X)
p + 13k = 2p + 10k p = 3k
From (i): 6k + 2k = 1 k = 18, p = 38
8p - 1 = 3 - 1 = 2
Answer: (1)
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