$\"\"$

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(a)

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The function $\"\"$ .

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If $\"\"$ is a probability density function then it must satisfy $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Since $\"\"$ , the function is probability density function for the spinner $\"\"$ s values.

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$\"\"$ for all $\"\"$ and $\"\"$ .

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$\"\"$

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(b)

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Find the mean by evaluating integral.

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Since the mean divides the area under a distribution into two equal parts and since in this case the distribution value is constant.

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The mean of any probability density function $\"\"$ is defined to be $\"\"$ .

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The function $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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(a) $\"\"$ for all $\"\"$ and $\"\"$ .

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(b) Mean $\"\"$ .