View Full Version : A continuous random variable

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.

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.

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