The value of C=1/3 for the probability density function f(x)=cx , 0<x<2.
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:
[tex]f(x)=cx\ \ at\ 0 < x < 2[/tex]
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
[tex]f(1)=c\times 1=c\\\\\\f(2)=c\times 2=2c\\\\[/tex]
So the probability density function is given as:
[tex]\sum f(x)=f(1)+F(2)=1\\\\\sum f(x)=c+2c=1[/tex]
[tex]3c=1\\\\c=\dfrac{1}{3}[/tex]
Hence the value of C=1/3 for the probability density function f(x)=cx , 0<x<2.
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