$\"\"$

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The function is $\"\"$ .

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(a)

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Show that $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ .

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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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Therefore, the non negative function is a probability density function.

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$\"\"$

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(b)

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Find $\"\"$ .

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The integral is $\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Therefore, $\"\"$ .

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$\"\"$

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(c)

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Find the value of $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

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Therefore, $\"\"$ .

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$\"\"$

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(a) $\"\"$ .

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(b) $\"\"$ .

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(c) $\"\"$ .