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Review of Algebra and Calculus

Section 00. Review of Algebra and Calculus. SOA/CAS Probability/Exam 1. Penn State classes: Math 140 Math 141 Math 230/231 Stat 414 3 hours, 35 questions, multiple choice Pass/fail, 0-10. Schedule. Oct 8– Sections 0 & 1 – Review of Algebra/Calculus & Basic Probability

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Review of Algebra and Calculus

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  1. Section 00 Review of Algebra and Calculus

  2. SOA/CAS Probability/Exam 1 • Penn State classes: • Math 140 • Math 141 • Math 230/231 • Stat 414 • 3 hours, 35 questions, multiple choice • Pass/fail, 0-10

  3. Schedule • Oct 8– Sections 0 & 1 – Review of Algebra/Calculus & Basic Probability • Oct 15 – Sections 2 & 3 – Conditional Probability & Combinatorial Principles • Oct 22– Sections 4 & 5 Random Variables and Probability Distributions & Distribution Parameters • Oct 29– Sections 6 & 7 – Discrete & Continous Distributions • Nov 5– Section 8 – Joint, Marginal and Conditional Distributions • Nov 12– Section 9 – Transformations of Random Variables • Nov 19– Section 10 – Risk Management Concepts • Nov 26 – No Class – Thanksgiving Break • Dec 3– Review

  4. Set Theory • A set is a collection of elements. • x A “x is an element of A” • Union: A B • All elements in A or B • Intersection: A B • All elements in both A and B • Complement: B’ • All elements not in B • Empty set: • Contains no elements

  5. Properties of Logarithms

  6. Differentiation • Product rule • Quotient rule • Chain rule • Partial differentiation • For f(x,y) to find differentiate for x and hold y constant.

  7. Integration • Double integrals • Calculate inside first • Doesn’t matter which is inside; make it easiest • Substitution • Sub , rewrite integral in terms of , solve, and sub back in • Integration by parts

  8. Geometric & Arithmetic Progressions • Geometric: for • If -1<r<1, the infinite series can be summed, • Arithmetic: for • Sum of first terms • Geometric is much more common

  9. Actex, Sec 0 #3, pg 26 A group of 1000 patients diagnosed with a certain disease is being analyzed with regard to the disease symptoms present. The symptoms are labeled A, B, and C, and each patient has at least one symptom. • 900 have either symptom A or B (or both) • 900 have either symptom A or C (or both) • 800 have either symptom B or C (or both) • 650 have symptom A • 500 have symptom B • 550 have symptom C Determine: • Number who had both symptoms A and B • Number who had either A or B (or both) but not C • Number who had all three symptoms

  10. Actex, Ex 0-14, pg 17 If for , then find and

  11. Actex, Sec 0 #13, pg 28 Calculate

  12. Actex, Sec 0 #14, pg 28 Smith begins a new job at a salary of 100,000 and expects to receive a 5% raise every year until he retires. Suppose that Smith works for 35 years. Determine the total salary earned over Smith’s career (to the nearest million).

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