Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is 0.33 (a couple willtravel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = thenumber of people who arrive late for the seminar.(a) Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] (Round your answers to four decimal places.)P(X = x)X012345678(b) Obtain the cumulative distribution function of X. (Round your answers to four decimal places.)X0123450.13500.13300.45350.25610.14650.04840.02810.01593.1356780.13500.26800.72150.9771112361.17201.20011.21604.531F(x)XXXXX

A random variable is the outcome of a random experiment. Typically, there are two types of random…

Answered: Three couples and two single…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider a cohort of patients receiving an experimental two-year treatment for a serious disease. Suppose that only 20% of the patients survive to the end of the second year. Assume CFM (constant force of mortality) within each year of treatment. Find the probability that a patient who survives the first four months dies by the end of the 20th month. Round to 4 decimal places.
A screening test for a particular infectious disease shows a positive test result in 90% of all cases when the disease is actually present, and in 10% of all cases when it is not. Assume that t% of the population is infected, where t is = 1. For a randomly chosen from the population person, find the probability that the person is actually infected if the test shows positive.
Suppose we roll 3 fair dice and let X be the number of twos we roll.(a) Find the probability mass function of X.(b) Find the expected value of X.(c) Find the variance of X.(d) Find the probability-generating function of X.(e) Find the moment-generating function of X
Show work for every step. Two types of customers (Preferred and Regular) call a service center. Preferred customers call with rate 3 per hour, and Regular customers call with rate 5 per hour. The interarrival times of the calls for each customer type are exponentially distributed. If the call center opens at 8:00 AM, what is the probability that the first call (regardless of customers type who calls) is received before 8:15 AM?
For each value of z*, find the cumulative probability P(Z s z*). (Round your answers to four decimal places.) AUSE SALT (a) z* = 1.96 (b) z* =-2.33 (c) z* = 2.58 (d) z* = 1.65
A family purchases a 2000 square foot home and plans to make extensions totalling 500 square feet. The house currently has a pool, and a real estate agent has reported that the house is in excellent condition. However, the house does not have a view, and this will not change as a result of the extensions. According to the results in column (1), what is the expected DOLLAR increase in the price of the home due to the planned extensions?
The service life T (this year) of a particular type of electric toothbrush is assumed to have the probability density f given by: see figure question (a) Find the probability that a randomly selected toothbrush (of this type) has a lifespan of more than 2 years.(b) Assume that a toothbrush of the same type has been working for one year already. What is the probability that it works for at least another 3 years?(c) What is the probability that the average lifespan of T¯ for 90 independent toothbrushes is greater than 2.1 years?
Three 3-sided dice are tossed. Each die has its sides labeled 0, 1, and 2. Let X denote the product of the outcomes of the threee dice. Determine the probability mass function (pmf) of X.
(a) Sketch the probability mass function of X . (b) Find the mean and standard deviation of the number of pots of olives sold daily. (c) If the profit obtained from selling a pot of olives is 50p, what is the expected profit made on a single day? During a working week of 6 days?
In each case, determine the value of the constant c that makes the probability statement correct. (Round your answers to two decimal places.) USE SALT (a) (c) = 0.9857 2.189 (b) P(0 ≤Z≤ c) = 0.3133 0.89 (c) P(C ≤ Z) = 0.1335 1.11 You may need to use the appropriate table in the Appendix of Tables to answer this question.
2. Suppose a coin having probability 0.7 of coming up heads is tossed three times. Let X denote thenumber of heads that appear in the three tosses.(a) List down the possible values of X.(b) Determine the probability mass function of X.
Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is 0.33 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar. (a) Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] (Round your answers to four decimal places.) 0 1 2 3 4 5 6 7 8 P(X=x) 0 1 2 3 4 5 6 7 0.1350 0.1330 0.2322 0.1965 0.2633 ✓ ✔ (b) Obtain the cumulative distribution function of X. (Round your answers to four decimal places.) F(x) 0.1350 0.268 0.5002 0.6967 x

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