For what value of an unknown is an Estimator Biased The application goes like this:

Let there be a random variable $X$, and $X_{1}, X_{2}, X_{3}$ random
  variables representing a sample of $X$ that has the same distribution
  as $X$ and that are independent of each other. In order to estimate
  the mean $m$ of the variable $X$, we use the following function:
  $$Y=0.6X_{1}+ 0.1X_{2}+ aX_{3}$$ with $a\in R$  
What is the condition so that Y is a biased estimator of the mean
  $m$ of $X$ ?

I know that for an estimator $\hat{p}$ to be unbiased the condition is that:
$$E(\hat{p})=p$$
But for $Y$ to be biased do we just write:
$$m \neq 0.6X_{1}+ 0.1X_{2}+ aX_{3}$$
And compute:
$$a \neq \frac{ -0.6X_{1}-0.1X_{2}+m }{ X_{3} }$$
Is this the condition? I'm not really sure about this. I just got this off the web and I read that the answer is $0.3$ I'm not sure if that's true. But if it is how do we get to that?
Thanks a lot.

We have $$E(Y) = 0.6E(X_1)+0.1E(X_2)+aE(X_3) = 0.6m+0.1m+am = (0.7+a)m.$$ In order for $Y$ to be an unbiased estimator of $m$, we need $E(Y)=m$ which is only the case if $a=0.3.$ So $Y$ is biased whenever $a\ne0.3.$
