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). The distribution function of the continuous random variable X is0,x< 3F(x) =1- kx 2 3x²a) Find the value of kb) Sketch the graph of F (x)c) Findi.Р(X < 4)ii.P(4 < X < 5)iii.Р(X > 6)d) Find the p.d.f of X

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The continuous random variable X has probability density function (pdf) 1 fx(x) 20 - 0 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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Question

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).

The distribution function of the continuous random variable X is
0,
x< 3
F(x) =
1- k
x 2 3
x²
a) Find the value of k
b) Sketch the graph of F (x)
c) Find
i.
Р(X < 4)
ii.
P(4 < X < 5)
iii.
Р(X > 6)
d) Find the p.d.f of X

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