# How to find the distribution of $B*=BSB^T$, where $S$ is the sample covariance from normal observations?

Let $X_1, X_2, \dots, X_{30}$ be a random sample of size $n=30$ from a $N_5(μ, Σ)$ population. If B is a $2\times 5$ matrix $$B = \begin{bmatrix} 1 & 0 & 1 & 0 & 1 \\ 1 & 0 & 0 & 0 & 1\end{bmatrix},$$ then what is the distribution of $B^\ast = B S B^T$, where $S$ is the variance-covariance matrix of sample observations?

• plz help me..I have little idea about covariance matrix? – Halima.Khatun Nov 13 '16 at 16:45
• I tried to clean up the formatting of your question, which was previously quite hard to read. You should check that I interpreted it properly. – djs Nov 13 '16 at 19:36
• Thank you for adding the [self-study] tag. Please read its wiki. Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. – gung - Reinstate Monica Nov 13 '16 at 19:58
• yes this is the actual problem.thanks for editing orginal format – Halima.Khatun Nov 16 '16 at 15:25