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kidia
04-10-2007, 06:51 PM
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
04-10-2007, 07:17 PM
Is that second 'a' supposed to be a 'b'?
\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
04-10-2007, 11:21 PM
Is that second 'a' supposed to be a 'b'?
\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
04-11-2007, 09:41 AM
variance E(X) = 4/45What does that mean?

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

kidia
04-11-2007, 03:57 PM
variance E(X) = 4/45What 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
04-11-2007, 11:56 PM
Makes no sense. Read it VERY carefully before you type it again.