F, the distribution function of a random variable X, is given by0t< -1-1 < t <00 < t < 1(1/12)t + 7/12 1≤t<21t> 2.(1/4)t + 1/4F(t) = 1/2(a) Sketch the graph of F.(b)Calculate the following quantities: P(X < 1), P(X = 1), P(1 ≤ X < 2),P(X > 1/2), P(X = 3/2), and P(1 < X ≤ 6).

For the given distribution function, we need to sketch the graph of F and find the required…

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A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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F, the distribution function of a random variable X, is given by 0 t< -1 (1/4)t + 1/4 -1 < t < 0 1/2 0 < t < 1 (1/12)t + 7/12 1 2. F(t) = 1 (a) Sketch the graph of F. (b) Calculate the following quantities: P(X < 1), P(X = 1), P(1 ≤ X < 2), P(X > 1/2), P(X = 3/2), and P(1 < X < 6).