The value of C=1/3 for the probability density function f(x)=cx , 0<x<2.
<h3>What is probability density function?</h3>
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:

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

So the probability density function is given as:


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