Consider that a game involves the spinning of a dial which is not fair. As the dial is not fair, after spinning it is more likely to point in any particular direction than another. Suppose that the movement of a dial, X, can be modelled by the following probability function f(x) = A sin x; 0

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Consider that a game involves the spinning of a dial which is not fair. As the dial is not fair, after spinning it is more likely to point in any particular direction than another. Suppose that the movement of a dial, ?, can be modelled by the following probability function...

 

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Consider that a game involves the spinning of a dial which is not fair. As the dial is not
fair, after spinning it is more likely to point in any particular direction than another.
Suppose that the movement of a dial, x, can be modelled by the following probability
function
f(x) = A sin x; 0 <x<a.
(i) Determine the value of A so that f (x) is a pdf (ii) Calculate E (X) and Var(X).
Transcribed Image Text:Consider that a game involves the spinning of a dial which is not fair. As the dial is not fair, after spinning it is more likely to point in any particular direction than another. Suppose that the movement of a dial, x, can be modelled by the following probability function f(x) = A sin x; 0 <x<a. (i) Determine the value of A so that f (x) is a pdf (ii) Calculate E (X) and Var(X).
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