Question

Suppose that x has the density function f(x) = cx 0 < x < 2 identify c

Answer 1

The value of C=1/3 for the probability density function f(x)=cx , 0<x<2.

What is probability density function?

The probability density function is a function of a continuous random variable, whose integral across an interval gives the probability that the value of the variable lies within the same interval.

Given that:

$f(x)=cx\ \ at\ 0 < x < 2$

Here we can see that the value of x is varies as 0,1,2

So at 0,1,2 the value of the function is

$f(1)=c\times 1=c\\\\\\f(2)=c\times 2=2c$

So the probability density function is given as:

$\sum f(x)=f(1)+F(2)=1\\\\\sum f(x)=c+2c=1$

$3c=1\\\\c=\dfrac{1}{3}$

Hence the value of C=1/3 for the probability density function f(x)=cx , 0<x<2.

To know more about probability density function follow

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