SOA - Exam P Questions With All Correct Answers

SOA - Exam P Questions With All
Correct Answers
Chapter 0
Topics mentioned in Chapter 0 that these flash cards do not cover: - Answer-- graphing
inequalities
- piecewise functions
- one to one functions
- limits and continuity
- basic rules of differentiation
- basic integration
- method of substitution

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For any two sets A and B, (A∩B)∪(A∩B') = - Answer-A

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Two sets A and B are disjoint if A∩B = - Answer-∅

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n(S) is defined to be - Answer-the number of elements in a set

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n(A∩B) + n(A∩B') = - Answer-n(A)

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In order to account for double counting, n(A∪B) = - Answer-n(A) + n(B) - n(A∩B)

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In order to account for double counting in three sets, n(A∪B∪C) = - Answer-n(A) + n(B)
+ n(C) - n(A∩B) - n(A∩C) - n(B∩C) + n(A∩B∩C)
(how does this work for a number of sets greater than three?)

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The inverse of a function ƒ(x) = y is - Answer-the function solved for x in terms of y,
such that if ƒ(x₀) = y₀, ƒ⁻¹(y₀) = x₀

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A quadratic function of the form ax² + bx + c = 0 can be solved with the quadratic
equation: - Answer-[-b ± √(b² - 4ac)] / 2a

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y = b^x ↔ log.b(y) = - Answer-x

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The natural logarithm is - Answer-log.e(y) = ln(y)

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Important properties of logarithms: - Answer-...

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Partial differentiation with respect to x is found by - Answer-differentiating with respect
to x and regarding y as a constant, then substituting in x₀ and y₀

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Antiderivatives of frequently used functions: - Answer-(for individual flash cards, see
other deck)

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Useful integration rules: - Answer-(for individual flash cards, see other deck)

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Integration by parts: - Answer-∫ v × du = v × u - ∫ dv × u

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∫ e^(ax) = - Answer-[axe^(ax) - e^(ax)] / a^2

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∫ xe^(ax) = - Answer-xe^(ax) / a - e^(ax) / a^2

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Geometric progression : a, ar, ar², ar³, ...
Sum of first n terms: - Answer-a + ar + ar² + ... + arⁿ⁻¹ = a[1 + r + r² + ... + rⁿ⁻¹] = a × (rⁿ-
1)/(r-1) = a × (1- rⁿ)/(1-r)

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∫ xⁿe^(-cx) = - Answer-n!/c^(n+1)

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Infinite sum of geometric series: - Answer-a/(1-r)

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Arithmetic progression: a, a +d, a + 2d, a + 3d, ...,
sum of first n terms - Answer-na + d × n(n-1)/2

/.Chapter 1
Topics mentioned in chapter 1 that these flash cards do not cover: - Answer-Definitions:
- event
- union of events

, - intersection of events
- complement
- continuous probability space

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Sample point - Answer-the simple outcome of a random experiment

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Probability space - Answer-the collection of all possible sample points related to a
specific experiment

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Mutually exclusive outcomes - Answer-cannot occur simultaneously (disjoint)
A∩B = ∅

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Exhaustive outcomes - Answer-outcomes that combine to be the entire probability
space, or equivalently, at least one of the outcomes must occur whenever the
experiment is performed
A₁∪A₂∪...∪A.n = S, the entire probability space

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Subevent (subset) - Answer-B contains all sample points in event A, then A is subevent
of B, A⊂B. The occurrence of A implies event B.

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Partition of A - Answer-C₁, C₂, C₃₃, ..., C.n form a partition of A if A = the union of all Cs
and the Cs are mutually exclusive

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DeMorgan's Laws:
(A∪B)' =
(A∩B)' = - Answer-(A∪B)' = A'∪B'
(A∩B)' = A'∩B'

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Indicator function for event A, I.A(x) = - Answer-I.A(x) = 1 if x ∈ A
I.A(x) = 0 if x ∉ A

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A∩(B₁∪B₂∪...∪B.n) =
A∪(B₁∩B₂∩...∩B.n) = - Answer-(A∩B₁)∪...∪(A∩B.n)
(A∪B₁)∩...∩(A∪B.n)

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If B₁...B.n are exhaustive events then for any event A, A = - Answer-(A∩B₁)∪...∪(A∩B.n)