Professor Hohn has an insurance policy on her car with a $500 deductible. This means that if she gets into an accident she will personally pay for 100% of the repairs up to $500, with the insurance company paying the rest. Suppose the the cost of repairs for the next accident is uniformly distributed between $100 and $1500. Let X denote the amount Professor John will have to pay. (a) Find the cumulative distribution function of X. (b) Compute the expected value of X. (c) Compute Var X a. Hint: Let Y be the total cost of repairs. Then, X, the amount Professor Hohn will have to pay, can we written as X " gpY q where

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)