I'm stuck on this problem:

Let a random vector $X$ be given in $\mathbb{R^{10}}$ with the standard scalar product. It is known that $\mathbb{E}[XX^T] = 5I_{10}$, $I_{10}$ – identity matrix of order 10. Let $t$ be a non-random vector of length 5 ($||t|| = 5$).

I need to solve this equation:

$$\mathbb{E}[X^TX] - \mathbb{E}\left(t^TX\right)^2$$

if I'm not mistaken then $\mathbb{E}[X^TX] = 5$. But I can't find the second term. Help me please

I'm stuck on this problem:

Let a random vector $X$ be given in $\mathbb{R^{10}}$ with the standard scalar product. It is known that $\mathbb{E}[XX^T] = 5I_{10}$, $I_{10}$ – identity matrix of order 10. Let $t$ be a non-random vector of length 5 ($||t|| = 5$).

I need to find the value of this expression:

$$\mathbb{E}[X^TX] - \mathbb{E}\left(t^TX\right)^2$$

if I'm not mistaken then $\mathbb{E}[X^TX] = 5$. But I can't find the second term. Help me please

I'm stuck on this problem:

Let a random vector $X$ be given in $\mathbb{R^{10}}$ with the standard scalar product. It is known that $\mathbb{E}[XX^T] = 5I_{10}$, $I_{10}$ – identity matrix of order 10. Let $t$ be a non-random vector of length 5 ($||t|| = 5$).

I need to solve equation:

$$\mathbb{E}[X^TX] - \mathbb{E}\left(t^TX\right)^2$$

if I'm not mistaken then $\mathbb{E}[X^TX] = 5$. But I can't find the second term. Help me please

I'm stuck on this problem:

Let a random vector $X$ be given in $\mathbb{R^{10}}$ with the standard scalar product. It is known that $\mathbb{E}[XX^T] = 5I_{10}$, $I_{10}$ – identity matrix of order 10. Let $t$ be a non-random vector of length 5 ($||t|| = 5$).

I need to solve this equation:

$$\mathbb{E}[X^TX] - \mathbb{E}\left(t^TX\right)^2$$

if I'm not mistaken then $\mathbb{E}[X^TX] = 5$. But I can't find the second term. Help me please