Joe Isley,the Owner of Big I HiFi,believes That the Store's

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The Answer is a.Rearranging the states gives: $a.Rearranging the states gives: Note, R = \left[ \begin{array} { r r } .05 & .08 \ .10 & 0 \end{array} ight] and Q = \left[ \begin{array} { c c } .67 & .20 \ .48 & .42 \end{array} ight] b.N = (I  Q)-1 = \left[ \begin{array} { r r } .33 & - .20 \ - .48 & .58 \end{array} ight] ^ { - 1 } To compute (I  Q)-1,first calculate its determinant, d = a11a22 - a21a12 = (.33)(.58) (-.48)(-.20)= .0954 Then, N = \left[ \begin{array} { c c } .58 / .0954 & .20 / .0954 \ .48 / .0954 & .33 / .0954 \end{array} ight] = \left[ \begin{array} { l l } 6.08 & 2.10 \ 5.03 & 3.46 \end{array} ight] c.The tree diagram is: Therefore,the probability of an item currently in stock being out of stock in two months is .13 + .08 = .21. d.The probability of eventually moving into each of the absorbing states from the nonabsorbing states is given by: NR = \left[ \begin{array} { l l } 6.08 & 2.10 \ 5.03 & 3.46 \end{array} ight] x \left[ \begin{array} { r r } .05 & .08 \ .10 & 0 \end{array} ight] Discontinued Clearance Sale NR = \begin{array} { c } ext { In Stock } \ ext { Out of Stock } \end{array} \left[ \begin{array} { c c } .51 & .49 \ .60 & .40 \end{array} ight] Hence,the probability of an item currently out of stock eventually being discontinued is .60.$ Note,
R =

\left[ \begin{array} { r r } .05 & .08 \.10 & 0\end{array} ight]

and Q =

\left[ \begin{array} { c c } .67 & .20 \.48 & .42\end{array} ight]

b.N = (I  Q)^-1 =

\left[ \begin{array} { r r } .33 & - .20 \- .48 & .58\end{array} ight] ^ { - 1 }

To compute (I  Q)^-1,first calculate its determinant,
d = a₁₁a₂₂ - a₂₁a₁₂ = (.33)(.58) (-.48)(-.20)= .0954
Then,
N =

\left[ \begin{array} { c c } .58 / .0954 & .20 / .0954 \.48 / .0954 & .33 / .0954\end{array} ight]

=

\left[ \begin{array} { l l } 6.08 & 2.10 \5.03 & 3.46\end{array} ight]

c.The tree diagram is: $a.Rearranging the states gives: Note, R = \left[ \begin{array} { r r } .05 & .08 \ .10 & 0 \end{array} ight] and Q = \left[ \begin{array} { c c } .67 & .20 \ .48 & .42 \end{array} ight] b.N = (I  Q)-1 = \left[ \begin{array} { r r } .33 & - .20 \ - .48 & .58 \end{array} ight] ^ { - 1 } To compute (I  Q)-1,first calculate its determinant, d = a11a22 - a21a12 = (.33)(.58) (-.48)(-.20)= .0954 Then, N = \left[ \begin{array} { c c } .58 / .0954 & .20 / .0954 \ .48 / .0954 & .33 / .0954 \end{array} ight] = \left[ \begin{array} { l l } 6.08 & 2.10 \ 5.03 & 3.46 \end{array} ight] c.The tree diagram is: Therefore,the probability of an item currently in stock being out of stock in two months is .13 + .08 = .21. d.The probability of eventually moving into each of the absorbing states from the nonabsorbing states is given by: NR = \left[ \begin{array} { l l } 6.08 & 2.10 \ 5.03 & 3.46 \end{array} ight] x \left[ \begin{array} { r r } .05 & .08 \ .10 & 0 \end{array} ight] Discontinued Clearance Sale NR = \begin{array} { c } ext { In Stock } \ ext { Out of Stock } \end{array} \left[ \begin{array} { c c } .51 & .49 \ .60 & .40 \end{array} ight] Hence,the probability of an item currently out of stock eventually being discontinued is .60.$ Therefore,the probability of an item currently in stock being out of stock in two months is .13 + .08 = .21.
d.The probability of eventually moving into each of the absorbing states from the nonabsorbing states is given by:
NR =

\left[ \begin{array} { l l } 6.08 & 2.10 \5.03 & 3.46\end{array} ight]

x

\left[ \begin{array} { r r } .05 & .08 \.10 & 0\end{array} ight]

Discontinued Clearance Sale
NR =

\begin{array} { c } ext { In Stock } \ ext { Out of Stock }\end{array} \left[ \begin{array} { c c } .51 & .49 \.60 & .40\end{array} ight]

Hence,the probability of an item currently out of stock eventually being discontinued is .60.

Joe Isley,the Owner of Big I HiFi,believes That the Store's

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Joe Isley,the Owner of Big I HiFi,believes That the Store's

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