Working with means and variances…. Expected Values… How does an insurance company determine its premiums? Weighs probability of “pay-out” against total.

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Presentation transcript:

Working with means and variances…

Expected Values… How does an insurance company determine its premiums? Weighs probability of “pay-out” against total revenue Determines cost per file by calculating yearly operating costs, amortizations and returns to shareholders Let’s consider question 4.79 in text and assume ahead of time that the insurance company must “make” $300 on this file to meet its financial targets. Is a premium of $250/a enough?

Life Insurance Premium… Why “negative”? Why does the earning cell become positive $1250 at age 26? (-$99,750)x( ) = -$ So, what’s the expected return?

Mean Value or Expected Value Value of Xx1x1 x2x2 x3x3 x4x4 Probabilityp1p1 p2p2 p3p3 p4p4

Rules for Means and Variances These sound scarier than they really are! Example: Suppose your mean income is $3200 and month and your spouse’s income is $2950 per month. What is your mean monthly family income? Rule 1:

You are sending weight data on Canadian grade 7 students to a colleague in Germany. The average weight is 104 lbs and you need to convert this to kg. Just before sending the data you discover that your grad student used a scale that overestimated all of the weights by 1.2 lbs. What average weight should you use in your study (expressed in kg)? (Hint: 1 lb = kg) Rule 2:

Rules for Variances… Remember – variance is just (standard deviation) 2 Variance is just another measure of scatter Value of Xx1x1 x2x2 x3x3 x4x4 Probabilityp1p1 p2p2 p3p3 p4p4 OK – this is scary!

Rules for handling variances… If you scale all numbers in a set by a fixed amount “b” and add a constant amount “a” (ie: a linear transformation) then: Rule 3:

Rules for handling variances… independent If X and Y are independent random variables, then: Rule 4:

Rules for handling variances… dependent If X and Y are dependent random variables that have a correlation of , then: Rule 4: Compare Examples 4.25 and 4.26 from text

Why does stats work? The law of large numbers…

In conclusion … There is a lot stuff in this section! Work through all of the examples in 4.4 Don’t memorize the formulas – instead try to “reason” them out in words – what do they mean Try the following questions: 4.60, 4.63, 4.67,4.83