The probability density function for the continuous random variableX is given by:(A(x² – 2x + 2) 0

Answered: s given by: (A(x² – 2x + 2) f(x) = ЗА 3

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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Question

The probability density function for the continuous random variable
X is given by:
(A(x² – 2x + 2) 0<x<3
3 <x < 4
otherwise
f(x) =
ЗА
%3D
Where A is a constant
a) Find the value of A
b) Find the cumulative distribution function F (x).
c) Show that the median of X lies between x = 2.6 and x = 2.7.
d) Find the mean and standard deviation of X

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Let X be a continuous random variable defined on interval $(- \infty, \infty)$ then, its probability density function (pdf) f(x) satisfies the following properties:

$f (x) \geq 0$
$\int_{- \infty}^{\infty} f (x) d x = 1$

The distribution function for the continuous variable is given by:

$F (x) = P (X \leq x) = \int_{- \infty}^{x} f (t) d t, - \infty < x < \infty$

Median is a positional average that divides the data set into two equal parts. It is the value that exceeds and is exceeded by the same number of observations. The median(m) of the probability density function f(x) is calculated using:

$F (x = m) = 0.5$