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)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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Let X be a point randomly selected from the unit interval [0, 1]. Consider the random variable Y = (1-X)-¹/2 (a) Sketch Y as a function of X. (b) Find and plot the cdf of Y. (c) Derive the pdf of Y. (d) Compute the following probabilities: P(Y > 1), P(3 < Y < 6), P(Y ≤ 10).

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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).