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13 February, 07:11

Professional basketball coaches may coach at one of three levels: Assistant, Associate, or Head. It is possible to transition from any of these levels (states) to another. Each of these three states is transient because once someone leaves coaching at any level they never return (at least according to our model). On average, annual salary for head coaches is $104,485, for associates is $62,993, and for assistants is $41,389. Using our P matrix, we have solved to find the fundamental matrix (we have called it the (I-Q) inverse matrix) : Assist Assoc Head Assist 6 4 2 Assoc 2 6 6 Head 1 2 10 For someone who is a head coach - what is their expected income for the remainder of their professional coaching career?

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  1. 13 February, 08:56
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    For someone who is a head coach - their expected income for the remainder of their professional coaching career will be

    Expected income = 1*$41,389 + 2*$62,993 + 10*$104,485

    Expected income = $1,212,225

    Step-by-step explanation:

    Professional basketball coaches may coach at one of three levels:

    Assistant Associate Head

    On average, the annual salary is given by

    Assistant = $41,389 Associate = $62,993 Head = $104,485

    Using our P matrix, we have solved to find the fundamental matrix (we have called it the (I-Q) inverse matrix):

    Assistant Associate Head

    Assistant 6 4 2

    Associate 2 6 6

    Head 1 2 10

    For someone who is a head coach - what is their expected income for the remainder of their professional coaching career?

    As per the given P matrix, for someone who is a head coach will be:

    Assistant = 1 time

    Associate = 2 times

    Head = 10 times

    Therefore, the expected income will be,

    Expected income = 1*$41,389 + 2*$62,993 + 10*$104,485

    Expected income = $1,212,225
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