The continuous random variable X has probability density function given byfx(x) = c(1 – x²),-1 1Also find Piii.Obtain the standard deviation of X, to 3 significant figures. The continuous random variable X has probability density function (pdf)fx(x)20- 0 < x<0Show that the cumulative distribution function (cdf) of X is0 + xFx (x)- 0 x).

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The continuous random variable X has probability density function given by fx(x) = c(1 – x²), -1 1 Also find P (-

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

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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Question

The continuous random variable X has probability density function given by
fx(x) = c(1 – x²),
-1<x< 1,
where c is a suitable constant.
i.
Show that c = ¾ and plot the graph of fx(x) against x.
ii.
Show that the cumulative distribution function of X is given by
х< -1
2 + 3x – x³
Fx (x) =
-1< x<1
4
1
x > 1
Also find P
iii.
Obtain the standard deviation of X, to 3 significant figures.

The continuous random variable X has probability density function (pdf)
fx(x)
20
- 0 < x<0
Show that the cumulative distribution function (cdf) of X is
0 + x
Fx (x)
- 0 <x<0
%D
20
Deduce an expression for P(X > x).

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