$\"\"$

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The function $\"\"$ and $\"\"$ if $\"\"$ or $\"\"$ .

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(a)

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Find the value of $\"\"$ .

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$\"\"$ is a probability density 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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$\"\"$

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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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(b)

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Find $\"\"$ .

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The probability that $\"\"$ lies between $\"\"$ and $\"\"$ is $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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The function $\"\"$ and $\"\"$ if $\"\"$ or $\"\"$ .

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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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$\"\"$ $\"\"$ .

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$\"\"$

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(c)

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Find the mean.

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

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$\"\"$ .

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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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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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(a) $\"\"$ .

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(b) $\"\"$ $\"\"$ .

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(c) $\"\"$ .