Question: The distribution function of a continuous random variable X is given by (i) Calculate the probabilities P(X 3), P(X 1), P(1 X

The distribution function of a continuous random variable X is given by F(t)= 0, t0, 4 ++ In (4). 0 4.

(i) Calculate the probabilities P(X ≤ 3), P(X ≥ 1), P(1 ≤ X ≤ 3).
(ii) Calculate the conditional probabilities P(X ≤ 3|X ≥ 1), P(X ≤ 4|X ≥ 1).
(iii) Find the density function of X.

F(t)= 0, t0, 4 ++ In (4). 0 4.

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