MAT136H1 Lecture Notes - Radian

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MAT136H1 Full Course Notes
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Question #2 (medium): forming a probability density function and its mean. Mean of a probability density function is given by ( ) Let ( : for what value of is ( ) a probability density function, for that value of , find ( , find the mean. Solution: in order for the function to be a probability density function, when it is integrated over all the possible values of x, it needs to add up to 1. Noting that it is in the form of . Plugging back into the limit: and this is equal to 1. , then : ( ) relates to. Remember to calculate the tangent inverse in the radian measure, because degree mode returns the answer in degree mode, which is not compatible with . Therefore, for the given pdf, ( : in order to find the mean, Since it is in in the form of chain rule: .

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