- Видео 95
- Просмотров 1 469
Eugene Lee
Канада
Добавлен 18 май 2023
In this channel, I aim to create an archive of Mathematics, Statistics, and Actuarial Science courses I am currently teaching or have taught throughout my career in colleges and universities. The archive includes lectures, tutorials, and problem-solving sessions, with notes and examples reorganized and restructured to reflect current and relevant topics, emphasizing more applications while minimizing theoretical aspects. For those of you who come across this channel, I hope you could find some helpful resources for your Math/Stat learning journey. While I will strive to update contents regularly, please understand that due to other commitments, frequent updates may not always be possible.
First-order ODE: Linear Equations #ordinarydifferentialequation
First-order ODE: Linear Equations #ordinarydifferentialequation
Просмотров: 14
Видео
SOA Exam P Practice Q50
Просмотров 87 часов назад
A random variable X has the cumulative distribution function F(x) = 0 for x less than 1, F(x) = (x^2-2x 3)/6 for x between 1 and 3, and F(x) = 1 for x greater than 3. Calculate the variance of X. [A similar question can be found in the official SOA website: www.soa.org]
SOA Exam P Practice Q49
Просмотров 89 часов назад
A two-component electrical system functions when at least one of its components is operational. Both components are operational today. The future operational lifetime of each component is exponentially distributed with mean three years. The lifetimes of the components are independent. The electrical system functions one year from now. Calculate the probability that both components will be opera...
SOA Exam P Practice Q48
Просмотров 216 часов назад
In a survey of job applicants, 20% apply for managerial positions, 30% apply for technical positions, and the other 50% apply for administrative positions. Six applicants are randomly selected. Calculate the expected number of selected applicants for technical positions, given that at least one of the selected applicants applies for managerial positions. [A similar question can be found in the ...
SOA Exam P Practice Q47
Просмотров 919 часов назад
The number of cars passing through a toll booth follows a distribution with the probability function p(x) = (1/3) (2/3)^x, x = 0, 1, 2, ... Calculate Var(X | X greater than 1) [A similar question can be found in the official SOA website: www.soa.org]
SOA Exam P Practice Q46
Просмотров 6День назад
The number of hours a student spends studying can be modeled by Z=2X 3Y−4. X and Y are independent random variables with Var(X) = 5 and Var(Y) = 6. Calculate Var(Z). [A similar question can be found in the official SOA website: www.soa.org]
SOA Exam P Practice Q45
Просмотров 8День назад
A manufacturing plant has five machines. Each year, each machine independently has an 90% probability of not breaking down. If a machine breaks down one or more times, the number of breakdowns is modeled by a geometric distribution with a mean of 1.25. The numbers of breakdowns for different machines are mutually independent. Each breakdown incur a repair cost of 10,000. Calculate the probabili...
SOA Exam P Practice Q44
Просмотров 2214 дней назад
The minimum force required to break a certain type of rope is normally distributed with a mean of 14,358 and a standard deviation of 50. A random sample of 300 ropes of this type is selected. Calculate the approximate probability that at least 255 of the selected ropes will not break under a force of 14,300. [A similar question can be found in the official SOA website: www.soa.org]
SOA Exam P Practice Q43
Просмотров 1414 дней назад
An international retail store manager monitors daily customer complaints, which can be modeled by a Poisson random variable with a mean of 10 complaints per day. Assume the complaints on different days are mutually independent. Calculate the probability, using the normal approximation, that the store receives at least 4,930 complaints during a period of 490 days. [A similar question can be foun...
SOA Exam P Practice Q42
Просмотров 514 дней назад
The lifetimes of smartphones of a certain model are exponentially distributed with a median of 1.8 years. Calculate the 93rd percentile of the lifetimes for these smartphones. [A similar question can be found in the official SOA website: www.soa.org]
SOA Exam P Practice Q41
Просмотров 814 дней назад
An insurance company insures a vintage motorcycle worth $20,000 for one year under a policy with a $2,000 deductible. During the policy year, there is a 0.05 chance of partial damage to the motorcycle and a 0.01 chance of a total loss of the motorcycle. If there is partial damage to the motorcycle, the amount X of damage (in thousands) follows a distribution with density function f(x)=0.2517exp...
SOA Exam P Practice Q40
Просмотров 721 день назад
A computer system is newly installed at the beginning of a calendar year. The time, in years, before the system experiences its first failure is exponentially distributed with mean 3. Calculate the probability that the system experiences its first failure in the last quarter of some calendar year. [A similar question can be found in the official SOA website: www.soa.org]
SOA Exam P Practice Q39
Просмотров 1321 день назад
A construction company has scheduled the start of a new project for July 1st. If it rains on July 1st the work is postponed and will begin on the next day that it does not rain. The company purchases insurance against rain. The policy will pay $1500 for each day, up to 2 days, that the start of the project is postponed. The insurance company determines that the number of consecutive days of rai...
SOA Exam P Practice Q38
Просмотров 321 день назад
Four packages containing gifts for different recipients are prepared along with accompanying boxes with labels. The packages are put into the boxes randomly. Calculate the probability that at least one package ends up in its accompanying box. [A similar question can be found in the official SOA website: www.soa.org]