Home » Posts tagged 'soa exam p cas exam 1 expected value variance standard deviation probability example solutions'

# Tag Archives: soa exam p cas exam 1 expected value variance standard deviation probability example solutions

### Categories

- Absolute Value (2)
- Absolute Value Equations (1)
- Absolute Value Inequalities (1)
- ACT Math Practice Test (2)
- ACT Math Tips Tricks Strategies (25)
- Addition & Subtraction of Polynomials (2)
- Addition Property of Equality (2)
- Addition Tricks (1)
- Adjacent Angles (2)
- Albert Einstein's Puzzle (1)
- Algebra (3)
- Alternate Exterior Angles Theorem (1)
- Alternate Interior Angles Theorem (2)
- Alternating Series (1)
- Altitude of a Triangle (2)
- Angle Addition Postulate (1)
- Angle Angle Side Theorem (1)
- Angle Angle Similarity Postulate (1)
- Angle Bisector Theorem (2)
- Angle Side Angle Theorem (1)
- Angles (28)
- Angles Parallel Lines Transversals (1)
- Application of Differentiation (6)
- Application of Integration (8)
- Arc Addition Postulate (1)
- Arc Length of a Curve Integration (1)
- Area as a Function of Length (1)
- Area between Curves Integration (2)
- Arithmetic & Geometric Sequence (1)
- Asymptotes of Rational Functions (1)
- Atoms Molecules Ions (2)
- Avogadro Gas Law (2)
- Balancing Chemical Equations (2)
- Base Angles Theorem (1)
- Binary Ionic Compound Formulas (2)
- Binomial Distribution (4)
- Binomial Theorem (2)
- Bounded Sequence (1)
- Boyle Gas Law (2)
- Business Calculus (1)
- Calorimetry (1)
- CASTC Theorem (1)
- Central Angle (2)
- Centroid (1)
- Chain Rule of Derivatives (1)
- Charles Gas Law (2)
- Chemical Reactions in Aqueous Solutions (5)
- Chemistry Matter and Measurement (2)
- Circles (3)
- Circumcenter (1)
- Combined Gas Law (2)
- Combined Variation and Proportion (1)
- Combining Like Terms in Polynomials (1)
- Commutative Property of Multiplication (1)
- Comparison Test (1)
- Completing the Square (2)
- Complex and Imaginary Numbers (2)
- Composition of Functions (2)
- Compound Interest (1)
- Conditional Expectation (1)
- Conditional Probability (2)
- Confidence Intervals (1)
- Conic Sections (1)
- Consecutive Exterior Angles Theorem (1)
- Consecutive Interior Angles Theorem (2)
- Continuity (3)
- Continuous Random Variable (8)
- Converse of Base Angles Theorem (1)
- Corresponding Angles Theorem (1)
- Covariance (1)
- CPCTC Theorem (1)
- CSSTP Theorem (1)
- Cumulative Distribution (1)
- Curve Sketching with Differentiation (2)
- Cylindrical Coordinates (1)
- Cylindrical Shell Integration Method (2)
- Decimal and Rational Number Operations (1)
- Derivative of Exponential Functions (3)
- Derivative of Hyperbolic & Inverse Hyperbolic Functions (3)
- Derivative of Inverse Functions (3)
- Derivative of Inverse Trigonometric Functions (3)
- Derivative of Logarithmic Functions (3)
- Differential Equations (10)
- Differentials (1)
- Dilation (1)
- Direct Variation and Proportion (1)
- Discrete Mathematics and Combinatorics (4)
- Discrete Random Variable (7)
- Disk Integration Method (2)
- Distributive Property of Multiplication (1)
- Division Property of Equality (2)
- Division Tricks (1)
- Domain and Range of a Function (1)
- Double Integrals (4)
- Eigenvalues and Eigenvectors (1)
- Ellipse (1)
- Empirical and Molecular Formula (2)
- Enthalpy Change (2)
- Equilateral Triangles (1)
- Euler (1)
- Expected Value (5)
- Exponential Distribution (1)
- Exponential Equations (3)
- Exponents (3)
- Exterior Angle Theorem (1)
- Exterior Angles (1)
- Factoring Polynomials (3)
- Financial Math (6)
- First Law of Thermodynamics (2)
- Fourier Series (1)
- Fraction Multiplication Rule (1)
- Fractions (7)
- Fundamental Theorem of Calculus (2)
- Gas Pressure (2)
- Gases in Chemistry (7)
- GED Math (4)
- Geometric Distribution (1)
- Geometric Formula as a Function (1)
- Geometric Formula Proof with Integration (2)
- Geometric Series (1)
- Geometry (14)
- Graph of Trigonometric Functions (2)
- GRE Math (4)
- Greatest Common Factor (1)
- Harmonic Series (1)
- Hydrostatic Force & Work (3)
- Hyperbola (1)
- Hypergeometric Distribution (2)
- Hypotenuse Leg Theorem (1)
- Hypothesis Testing (1)
- Ideal Gas Law (2)
- Identity Property of Multiplication (1)
- Implicit Differentiation (7)
- Improper Integrals (7)
- Incenter (1)
- Increasing or Decreasing Sequence (1)
- Independent Events Probability (1)
- Infinite Sequences (8)
- Infinite Series (19)
- Infinite Series Derivative (1)
- Inscribed Angle (1)
- Integral Test (1)
- Integration by Partial Fraction Decomposition (6)
- Integration by Parts (6)
- Integration by Trigonometric Substitution (5)
- Integration of Exponential Functions by Substitution (5)
- Integration of Functions with Roots & Fractions (5)
- Integration of Hyperbolic & Inverse Hyperbolic Functions by Substitution (5)
- Integration of Inverse Trigonometric Functions by Substitution (5)
- Integration of Logarithmic Functions by Substitution (5)
- Integration of Trigonometric Functions by Substitution (5)
- Integration with Reduction Formula (1)
- Interior Angles (2)
- Inverse Functions (2)
- Inverse Trigonometric Functions (1)
- Inverse Variation and Proportion (1)
- Isosceles Triangles (1)
- Joint Distribution (1)
- Joint Moment Generating Functions (1)
- Joint Variation and Proportion (1)
- Kite (1)
- Lattice Multiplication (1)
- Law of Combining Volumes (2)
- Law of Cooling (1)
- Law of Cosines (1)
- Law of Sines (1)
- Laws of Chemical Combination (2)
- Least Common Multiple (1)
- Limit Comparison Test (1)
- Limit Definition of Derivative (3)
- Limiting Reactants (2)
- Limits (10)
- Line Segments (1)
- Linear Algebra (6)
- Linear Approximation (2)
- Linear Equations (3)
- Linear Functions (1)
- Linear Measure (1)
- Linear Pair Angles Theorem (2)
- Locus of Points (1)
- Logarithmic Differentiation (2)
- Logarithmic Equations (1)
- Logarithms (4)
- Maclaurin Series (1)
- Mass Percent Composition from Chemical Formulas (2)
- Math Puzzles (2)
- Math Tricks (7)
- Matrices (5)
- Mean Value Theorem for Integrals (1)
- Means-Extremes Property of Proportions (2)
- Median of a Triangle (1)
- Midsegment Theorem (1)
- Molar Mass (2)
- Molarity of Compounds and Ions (2)
- Mole and Avogadro's Number (2)
- Molecular and Formula Mass (2)
- Moment Generating Function (2)
- Multiple Integrals (2)
- Multiplication Property of Equality (2)
- Multiplication Tricks (1)
- Multivariable Calculus (5)
- Music Theory (3)
- Negative Binomial Distribution (1)
- Negative Exponents (1)
- NonLinear Equations (8)
- NonLinear Inequalities (2)
- Normal Approximation (1)
- Normal Distribution (3)
- Nth Term Test (1)
- Number Line (5)
- Optimization (4)
- Orthocenter (2)
- Oxidation and Reduction in Chemical Reactions (2)
- P Series (1)
- Parabola (3)
- Parametric Equations and Curves (2)
- Partial Derivatives (2)
- Partial Fraction Decomposition (1)
- Particle Motion (1)
- Pascal's Triangle (1)
- Percentage Probability (1)
- Perimeter as a Function of Area (1)
- Permutations and Combinations (1)
- Perpendicular Bisector Theorem (1)
- Physics (1)
- Piecewise Probability Distribution Functions (4)
- Plane (1)
- Poisson Distribution (2)
- Polar Coordinates (2)
- Polynomial Multiplication (1)
- Power Rule of Derivatives (5)
- Power Series (1)
- Precalculus (2)
- Precipitate Formation in Chemical Reactions (2)
- Principle of Mathematical Induction (1)
- Probability & Statistics (25)
- Probability of Outcomes (1)
- Product Rule of Derivatives (1)
- Projectile Motion (3)
- Puzzles (6)
- Quadratic Equations (3)
- Quadratic Formula (1)
- Quadratic Functions (2)
- Quadratic Inequalities (1)
- Quotient Rule of Derivatives (1)
- Radians Degrees Minutes Seconds (2)
- Radicals (1)
- Rational and Radical Expressions (3)
- Rational Equations (1)
- Rational Inequalities (1)
- Rational Numbers (2)
- Reactions of Acids and Bases (2)
- Reciprocal Rule of Division (1)
- Rectangles (1)
- Reference Angles (1)
- Reflection (2)
- Reflexive Property (1)
- Related Rates (3)
- Riemann Sum (20)
- Right Triangles (1)
- Rotation (2)
- Rotation of Axes (1)
- Rule of Product (1)
- Russian Peasant Multiplication (1)
- SAT Math Practice Test #1 (59)
- SAT Math Practice Test #2 (59)
- SAT Math Practice Test #3 (59)
- SAT Math Practice Test #4 (59)
- SAT Math Practice Test #5 (30)
- SAT Math Practice Test #6 (25)
- SAT Math Practice Test #7 (12)
- SAT Math Practice Test #8 (3)
- Scientific Notation (2)
- Segment Addition Postulate (1)
- Side Angle Side Theorem (1)
- Side Side Side Theorem (1)
- Sidelight Division (1)
- Significance Tests (1)
- Significant Figures (2)
- Similarity of Triangles (1)
- SOA Exam P (4)
- Solve for X (2)
- Specific Heat (1)
- Spherical Coordinates (1)
- Square Number (1)
- Squares (1)
- Standard Deviation (3)
- Stoichiometry Chemical Calculations (8)
- Substitution Property of Equality (2)
- Subtraction Property of Equality (2)
- Summation Formulas (2)
- Supplementary Angle Theorem (1)
- Surface Area Integration (2)
- Symmetric Property (2)
- Symmetry Tests (1)
- Synthetic and Long Division of Polynomials (1)
- System of NonLinear Equations (1)
- Systems of Linear Equations (1)
- T Distribution (1)
- Table Data (3)
- Table of Ordered Pairs (1)
- Taylor Series (1)
- Telescoping Series (1)
- Theoretical & Proofs (5)
- Thermochemistry (3)
- Titrations in Chemical Reactions (2)
- Transformation (5)
- Transitive Property (2)
- Translation (1)
- Trapezoid (1)
- Tree Diagram Probability (1)
- Triangles (22)
- Trigonometric Angle Sum Difference Multiple Half-Angle Formulas (3)
- Trigonometric Equations (4)
- Trigonometric Form of Complex Numbers (1)
- Trigonometric Functions (4)
- Trigonometric Identity Proofs (1)
- Trigonometry (19)
- Triple Integrals (1)
- Truth Tables (1)
- Two Column Proofs (2)
- Two Way Table (1)
- Uniform Distribution (1)
- Unit Circle (5)
- Unit Conversions (2)
- Variance (2)
- Variation and Proportion (4)
- Vectors (1)
- Vectors in the Plane (2)
- Venn Diagram (1)
- Vertex Form of a Parabola (1)
- Vertical Angles Theorem (2)
- Volume of the Solid of Revolution (2)
- Washer Integration Method (2)
- Whole Number Operations (3)
- World's HARDEST Easy Geometry problems (1)
- Wronskian (1)
- Yield of Chemical Reactions (2)

## SOA Exam P CAS Exam 1 Expected Value Variance Standard Deviation probability problems

March 26, 2019 / 4 Comments on SOA Exam P CAS Exam 1 Expected Value Variance Standard Deviation probability problems

**Multiple Moment Generating Functions MGF example question**

A company insures homes in three cities, J, K and L. Since sufficient distance separates the cities, it is reasonable to assume that the losses occurring in these cities are independent. The moment generating functions for the loss distributions of the cities are

Let *X* represent the combined losses from the three cities. Calculate .

Solution to this Society of Actuaries **Exam P** practice problem is given in the video below!

**Expected Value & Probability Density Function PDF example problem**

Let *X* be a continuous random variable with density function

{

Calculate the expected value of *X*.

Solution to this Society of Actuaries **Exam P** practice problem is given in the video below!

**Moment Generating Function MGF example**

Let *X*_{1}* ,* *X*_{2}* , X*_{3} be a random sample from a discrete distribution with probability function

{

Determine the moment generating function, *M*(*t*), of .

Solution to this Society of Actuaries **Exam P** practice problem is given in the video below!

**Expected Value & Probability Density Function PDF word problem**

An insurance company’s monthly claims are modeled by a continuous, positive random variable *X*, whose probability density function is proportional to

Determine the company’s expected monthly claims.

Solution to this Society of Actuaries **Exam P** practice problem is given in the video below!

**Percentiles & Probability Density Function PDF example question**

An insurer’s annual weather related loss, *X*, is a random variable with density function

{

Calculate the difference between the 30th and 70th percentiles of *X*.

Solution to this Society of Actuaries **Exam P** practice problem is given in the video below!

**Standard Deviation & Moment Generating Function MGF example problem**

An actuary determines that the claim size for a certain class of accidents is a random variable, *X*, with a moment generating function

Determine the standard deviation of the claim size for this class of accidents.

Solution to this Society of Actuaries **Exam P** practice problem is given in the video below!

**Standard Deviation Table example**

A probability distribution of the claim sizes for an auto insurance policy is given in the table below:

Claim Size |
20 | 30 | 40 | 50 | 60 | 70 | 80 |

Probability |
.15 | .10 | .06 | .20 | .10 | .10 | .30 |

What percentage of the claims are within one standard deviation of the mean claim size?

Solution to this Society of Actuaries **Exam P** practice problem is given in the video below!

**Variance & Cumulative Distribution Function CDF example question**

A random variable has the cumulative distribution function

{

Calculate the variance of *X*.

Solution to this Society of Actuaries **Exam P** practice problem is given in the video below!

**Variance word problem**

A recent study indicates that the annual cost of maintaining and repairing a car in a town to Ontario averages 200 with a variance of 260. If a tax of 20% is introduced on all items associated with the maintenance and repair of cars (i.e., everything is made 20% more expensive), what will be the variance of the annual cost of maintaining and repairing a car?

Solution to this Society of Actuaries **Exam P** practice problem is given in the video below!

### Recent Posts

- Angular Speed and Linear Speed problems March 13, 2024
- Converting Repeating Decimals to Fractions problems February 29, 2024
- Geometry Puzzles and Brain Teasers December 18, 2023
- VERIFYING Whether Given Two Functions are Inverses December 15, 2023
- Trigonometric Functions WORD problems December 11, 2023
- Null Hypothesis Testing statistics problems February 9, 2021
- Variance problems February 9, 2021
- Confidence Interval statistics problems December 9, 2020
- Greatest Common Factor and Least Common Multiple problems December 3, 2020
- Translation Geometry problems December 1, 2020

### Archives

- March 2024 (1)
- February 2024 (1)
- December 2023 (3)
- February 2021 (2)
- December 2020 (4)
- November 2020 (4)
- October 2020 (12)
- September 2020 (10)
- August 2020 (2)
- July 2020 (9)
- June 2020 (2)
- May 2020 (22)
- April 2020 (5)
- November 2019 (1)
- May 2019 (409)
- April 2019 (62)
- March 2019 (63)

S | M | T | W | T | F | S |
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | |

7 | 8 | 9 | 10 | 11 | 12 | 13 |

14 | 15 | 16 | 17 | 18 | 19 | 20 |

21 | 22 | 23 | 24 | 25 | 26 | 27 |

28 | 29 | 30 |

## Recent Comments