Respuesta :
Answer:
[tex]S^4=\left[\begin{array}{ccc}0.56875&0.43125\end{array}\right][/tex]
Step-by-step explanation:
[tex]\text{Initial-State Matrix}, S_0=\left[\begin{array}{ccc}0.1&0.9\end{array}\right][/tex]
[tex]\text{Transition Matrix}, P=\left[\begin{array}{ccc}0.8&0.2\\0.3&0.7\end{array}\right][/tex]
First, we are to determine [tex]P^4[/tex].
[tex]P^2=\left[\begin{array}{ccc}0.8&0.2\\0.3&0.7\end{array}\right]\left[\begin{array}{ccc}0.8&0.2\\0.3&0.7\end{array}\right]=\left[\begin{array}{ccc}0.8*0.8+0.2*0.3&0.8*0.2+0.2*0.7\\0.3*0.8+0.7*0.3&0.3*0.2+0.7*0.7\end{array}\right]\\\\=\left[\begin{array}{ccc}0.7&0.3\\0.45&0.55\end{array}\right][/tex]
[tex]P^4=(P^2)^2=\left[\begin{array}{ccc}0.7&0.3\\0.45&0.55\end{array}\right]\left[\begin{array}{ccc}0.7&0.3\\0.45&0.55\end{array}\right]\\=\left[\begin{array}{ccc}0.7*0.7+0.3*0.45&0.7*0.3+0.3*0.55\\0.45*0.7+0.55*0.45&0.45*0.3+0.55*0.55\end{array}\right]\\\\=\left[\begin{array}{ccc}0.625&0.375\\0.5625&0.4375\end{array}\right][/tex]
Therefore:
[tex]S^4=S_0P^4[/tex]
[tex]=\left[\begin{array}{ccc}0.1&0.9\end{array}\right]\left[\begin{array}{ccc}0.625&0.375\\0.5625&0.4375\end{array}\right]\\=\left[\begin{array}{ccc}0.1*0.625+0.9*0.5625&0.1*0.375+0.9*0.4375\end{array}\right]\\\\S^4=\left[\begin{array}{ccc}0.56875&0.43125\end{array}\right][/tex]
Answer:
CaCl2, MgO, Na2O
Step-by-step explanation:
Got it right on edg. 2020
