C1. Let X be a continuous random variable with PDF f(x) = (2-x) for −1≤ x ≤ c and f(x) = 0 otherwise. (a) Explaining your work, find the value of the constant c. (b) What is P(X > 1)? (c) Calculate the expectation of X. (d) Calculate the variance of X.
C1. Let X be a continuous random variable with PDF f(x) = (2-x) for −1≤ x ≤ c and f(x) = 0 otherwise. (a) Explaining your work, find the value of the constant c. (b) What is P(X > 1)? (c) Calculate the expectation of X. (d) Calculate the variance of X.
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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could you please do all the parts written out with explanations
Transcribed Image Text:C1. Let X be a continuous random variable with PDF
f(x) = ²(2-x)
for −1≤ x ≤ c
and f(x) = 0 otherwise.
(a) Explaining your work, find the value of the constant c.
(b) What is P(X > 1)?
(c) Calculate the expectation of X.
(d) Calculate the variance of X.
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