Isn't it a Binomial law?

Question

Let $\Omega =\{0,2,4,...,20\}$ and $X$ s.t. $$\mathbb P\{X=2k\}=\binom{10}{k}p^k(1-p)^{n-k},$$ for $k\in\{0,...,10\}$ and $p\in (0,1)$. For me it follows a Binomial law, but my teacher say that it doesn't and I don't understand why. Could someone explain why it's not a Binomial law ? For me it's however exactly the definition of the Binomial Law.

Answer 1

As you can see in the link you put, the support must be $\Omega =\{0,1,...,10\}$ which is not the cas in your situation. In your case, you will get $\mathbb E[X]=20p$ instead of $\mathbb E[X]=10p$ what would have been needed in case $X$ would have followed Binomial distribution. However, notice that you can define $Y\sim Binom(p,10)$ s.t. $X=2Y$.