Question 5A population of healthy people over the year of age 50 to51 is subject to a constant force of decrement due to sickness of 0.08 per annum, and aconstant force of mortality of 0.002 per annum. Assume that a double decrementmodel is used.(a) Calculate the probability that a healthy person aged exactly 50 will still behealthy at exact age 51.(b) Calculate the probability that a healthy person aged exactly 50 will die due toany cause other than from sickness before exact age 51.(c) Calculate the independent probability of a life aged exactly 50 dying beforeexact age 51.TE[

In actuarial science, understanding the probability of different events occurring in a population is…

Answered: Question 5 A population of healthy…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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13 An experiment compares two bacterial cultures, both growing exponentially. Culture A begins with 1000 bacteria present at noon and at 2 p.m. there 1650 bacteria. Culture B also begins with 1000 bacteria, but is started at I p.m. and by 2 p.m. there are 1350 bacteria. Is there a time when the two cultures have the same number of bacteria?
Changes in the earth's rotation are exceedingly small. However, a very long-term trend could be important. (Reference: Journal of Astronomy, Vol. 57, pp. 125-146.) Let I represent an increase and D a decrease in the rate of the earth's rotation. The following sequence represents historical increases and decreases measured every consecutive fifth year. D D D D D D I I D D D D D I I I I I I I I I I D I I I I I Test the sequence for randomness. Use ? = 0.05. (a) What is the level of significance? (b) Find the sample test statistic R, the number of runs. (c) Find the upper and lower critical values in the Critical Values for Number of Runs R table.
Question 5 The life time of an electrical part follows an exponential distribution with mean of 5 years. Calculate the probability the life of the part is less than two years. O .67 .33
A survey was conducted and asked: "Do you consider your health to be poor?" This was coded as 1 for "yes" and 0 for "no." The effect of age (in years) and sex (1 male, 0 = female) on the outcome was examined using logistic regression. The fitted logistic model is: = logit(ô) = −0.544 + ß * sex + 0.0331 * age (a) What are the odds of responding "yes" for a female subject who is 60 years old? (b) What is the estimated odds ratio corresponding to the age variable? Interpret this estimate. (c) Suppose that, based on the data from the survey, the odds of responding "yes" for males are 3.79% greater than the odds for females, adjusting for age. What is the value of Â? (d) If we only wanted to assess the association between survey response (yes/no) and sex, what other method(s) (that we have learned in this class) could we have used (name at least one)? In your own words, explain why we cannot use the same method(s) if we want to consider the effects of both sex and age on survey response.
#11 Find (Z=)
QUESTION 3 Suppose there are two football teams A and B. In recent matches Team A has a mean of 1 goal per match and Team B has a mean of 2 goals per match. Suppose that the probability of the number of goals scored by a team obeys a Poisson Distribution In the following questions, give the reasoning behind your answers. You can express some answers in terms of logarithms. Q 3(d) What is the most probable score line? Q 3(e) In a particular match, over how long a time period would the probability of no goals be 20%?
Question 1 Explain why normalizing equation is needed in steady state probability calculations in your own words.
QUESTION 1 The same scenario is used for all questions. New parents in a little town buy two major brands of infant formulas, labeled A and B. After some intensive study, a marketing researcher for one of the manufacturers found that the probability of parents purchasing A or B is based on the parents' most recent purchase. Suppose that the following transition probabilities are appropriate O Probabilities of Parents Purchasing A or B From A To A To B O A B B Which of the following is the correct two period tree diagram for a customer who last purchased Brand A? O A 0.75 A 0.20 0.25 0.75 0.75 0.25 0.25 0.75 A B A B A 0.25 B 0.80 0.75 0.25 0.20 0.80 0.75 0.25 0.20 0.80 0.25 0.75 0.20 0.80 A B A B A B A B A B A B (0.25)(0.75)-0.1875 (0.25)(0.25) 0.0625 (0.75)(0.20) 0.1500 (0.75)(0.80)-0.6000 (0.75)(0.75)=0.5625 (0.75)(0.25)-0.1875 (0.25)(0.20)-0.0500 (0.25)(0.80)-0.2000 (0.25)(0.25) 0.0625 (0.25)(0.75)-0.1875 (0.75)(0.20) 0.1500 (0.75)(0.80) 0.6000
A medical test has been designed to detect the presence of a certain disease. Among people who have the disease, the probability that the disease will be detected by the test is 0.94. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.03. It is estimated that 5% of the population who take this test have the disease. (Round your answers to three decimal places.) (a) If the test administered to an individual is positive, what is the probability that the person actually has the disease?(b) If an individual takes the test twice and the test is positive both times, what is the probability that the person actually has the disease? (Assume that the tests are independent.)
An article in the European Physical Journal B ["Evidence for the exponential distribution of income in the USA" (2001, Vol. 20, pp. 585- 589)] shows that individual income in the US can be approximated with an exponential distribution. Suppose that the mean of individual income in a year is $25000. eTextbook and Media (b) What percentage of individuals in the US earn less than $20000? Round your answer to three decimal places (e.g. 0.987). P(X 50000) = (d) What is the income exceeded by 1% of individuals? Round your answer to the nearest integer (e.g. 9876). x =
Question 3 The life time of an electrical part follows an exponential distribution with mean of 7 years. Calculate the probability the life of the part is less than two years. .24 .76 .13 .87

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