Continuous random variable X has density given by f(x)=c⋅(x+1)*(x−3) if x∈[−1,3] and 0 otherwise.
1) Find DF(2;X) . distribution function
2) Find E[X] .

Question

Continuous random variable   X   has density given by   f(x)=c⋅(x+1)*(x−3)   if   x∈[−1,3]   and   0   otherwise.
1) Find   DF(2;X) . distribution function 
2) Find   E[X] .

zarkon · Answer

what have you tried?

anonymous · Answer

i try to use the integral by putting this together as  x^2-2x-3

irishboy123 · Answer

$f(x)=c(x+1)(x−3)$
$F(x) = \int\limits_{-1}^{3} \; dx  \quad c(x^2-2x-3)$

anonymous · Answer

$$\frac{ x^3 }{ 3 }- x^2 -3x$$

irishboy123 · Answer

for the next bit, you might try $G(x) = \int\limits_{-1}^{3} \; x \; dx  \quad c(x^2-2x-3) =  \int\limits_{-1}^{3}  \; dx  \quad c(x^3-2x^2-3x)$

anonymous · Answer

ok

zarkon · Answer

you need to find the value of $c$ such that 

$$\int\limits_{-1}^{3}   c(x^2-2x-3)dx=1$$

anonymous · Answer

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