Consider a continuous random variable X with the following PDF: {: -1 ≤ x ≤0 or 1≤ x ≤ 3 otherwise (a) Sketch the PDF of X. Be sure to label your axes. (b) Determine the value of c that satisfies the normalization property. Set c to this value for the remainder of the problem. This can be done without integration, so your answer should be a number. fx(x) (c) What is the expected value of X? (d) What is the variance of X? (e) What is E[2X² - 3X + 1]? (f) Calculate the probability that X| is less than 2. (Your answer can be an integral, but you can also take advantage of the simple structure of the PDF.) (g) Let B = (−2,2). Determine the conditional PDF fx|Â(x) of X given the event {X € B}. (h) Calculate the probability that X < 0 given that X is less than 2. (i) Calculate the conditional expectation E[X|B] of X given that X is less than 2.

Consider a continuous random variable X with the following PDF: {: -1 ≤ x ≤0 or 1≤ x ≤ 3 otherwise (a) Sketch the PDF of X. Be sure to label your axes. (b) Determine the value of c that satisfies the normalization property. Set c to this value for the remainder of the problem. This can be done without integration, so your answer should be a number. fx(x) (c) What is the expected value of X? (d) What is the variance of X? (e) What is E[2X² - 3X + 1]? (f) Calculate the probability that X| is less than 2. (Your answer can be an integral, but you can also take advantage of the simple structure of the PDF.) (g) Let B = (−2,2). Determine the conditional PDF fx|Â(x) of X given the event {X € B}. (h) Calculate the probability that X < 0 given that X is less than 2. (i) Calculate the conditional expectation E[X|B] of X given that X is less than 2.

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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