A continuous random variable

[kidia]

Any help in this question will be appreciated,A continuous random variable X has p.d.f
f(x)=
{a+ax+cx^2, 0<=x<=1}
{0 ,elsewhere.

If E(X)=3/4 and variance E(X) = 4/45.Find the values of a,b and c.

 

[pka]

Is that second 'a' supposed to be a 'b'?
\(\displaystyle \L\begin{array}{l}
\int\limits_0^1 {\left( {a + ax + cx^2 } \right)dx} = 1 \\
\int\limits_0^1 {x\left( {a + ax + cx^2 } \right)dx} = \frac{3}{4} \\
\int\limits_0^1 {x^2 \left( {a + ax + cx^2 } \right)dx} = \frac{4}{{45}} \\
\end{array}.\)

 

[kidia]

Is that second 'a' supposed to be a 'b'?
\(\displaystyle \L\begin{array}{l}
\int\limits_0^1 {\left( {a + ax + cx^2 } \right)dx} = 1 \\
\int\limits_0^1 {x\left( {a + ax + cx^2 } \right)dx} = \frac{3}{4} \\
\int\limits_0^1 {x^2 \left( {a + ax + cx^2 } \right)dx} = \frac{4}{{45}} \\
\end{array}.\)

Sorry,is true the second one supposed to be b I have made the typing error,thanks very much pka

 

[tkhunny]

variance E(X) = 4/45

What does that mean?

Do you mean Var(x) = 4/45 or E[x^2] = 4/45 or somethign else?

 

[kidia]

variance E(X) = 4/45

What does that mean?

Do you mean Var(x) = 4/45 or E[x^2] = 4/45 or somethign else?

It mean variance of E(x).

 

[tkhunny]

Makes no sense. Read it VERY carefully before you type it again.