In Exercise 5.3, we determined that the joint probability distribution of Y1, the number ofmarried executives, and Y2, the number of never-married executives, is given byOO.()33 — У1 — У2P(y1, y2) :where y, and y2 are integers, 0 < yı < 3,0 < y2 < 3, and 1 < y1 + y2< 3.a Find the marginal probability distribution of Y1, the number of married executives amongthe three selected for promotion.b Find P(Y1 = 1|Y2 = 2).c If we let Y3 denote the number of divorced executives among the three selected for promo-tion, then Y3 = 3 – Y1 – Y2. Find P(Y3 = 1|Y2 = 1).

a)The joint probability distribution of Y1 , the number of married executives and Y2, the number of…

Answered: In Exercise 5.3, we determined that the…

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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Oxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area. In this wetland environment, the mean oxygen demand was u = 9.3 mg/L with 95% of the data ranging from 6.7 mg/L to 11.9 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal. In USE SALT (a) Use the 95% data range to estimate the standard deviation for oxygen demand. (b) An oxygen demand below 8 indicates that some organisms in the wetland environment may be dying. What is the probability that the oxygen demand will fall below mg/L? (Round your answer to four decimal places.) (c) A high oxygen demand can also indicate trouble. An oxygen demand above 12 may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed…
4. The battery life of a fully charge iPhone 13 Pro on a standby follows a normally distributed with mean 7 hour and variance o² fl = 1 hours. = (a) Write out the integral form of the probability that a fully-charged iPhone 13 Pro last between 7 and 9 hours on standby. then use the pnorm function in R to find this probability. (b) What is the probability that a fully-charged iPhone 13 Pro last less than 5 hours? (c) What is the probability that a fully-charged iPhone 13 Pro last more than 9 hours? (d) What is the minimum time a fully-charged iPhone 13 Pro need to last in order to be in the top 10% best quality?
Let X represent the number of homes a real estate agent sells during a given month. Based on previous sales records, she estimates that P(0)= 0.62, P(1)= 0.21, P(2)= 0.13, P(3)= 0.03, P(4)= 0.01, with negligible probability for higher values of x. Find the long-term average number of homes the real estate agent expects to sell each month.
The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.6 and B = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.7520 0.7520 0.1065 x X X (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 0.6312 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) 191 Xhr
Suppose you were given this Joint Probability Distribution: x=number of bars of signal strength x=number of bars of signal strength x=number of bars of signal strength x=number of bars of signal strength y=number of times city name is stated 1 2 3 Marginal probability distribution of y 4 0.15 0.1 0.05 0.3 3 0.02 0.1 0.05 0.17 2 0.02 0.03 0.2 0.25 1 0.01 0.02 0.25 0.28 0.2 0.25 0.55 Marginal probability distribution of x Marginal probability distribution of x Marginal probability distribution of x Marginal probability distribution of x Find the conditional mean and variance of Y|3 Mean = Variance =
Oxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area. In this wetland environment, the mean oxygen demand was μ = 9.9 mg/L with 95% of the data ranging from 6.3 mg/L to 13.5 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal. (a) Use the 95% data range to estimate the standard deviation for oxygen demand. (b) An oxygen demand below 8 indicates that some organisms in the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L? (Round your answer to four decimal places.) (c) A high oxygen demand can also indicate trouble. An oxygen demand above 12 may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed 12…
1. Provide the graphs for PDF and CDF of the random variable B which takes on values of 1 and 0 with probability of 0.40 and 0.60. (Don't forget the horizontal axis must be sorted).
The number of students who fail per semester is often modeled as a Poisson random variable. Assume that on the average there are 5 students who fail per sem. d. If exponential distribution can model this system, what is the probability that there will be no failing students right after midterm? Let X denote the time in semesters from the start of the interval until the first failure and that a semester is divided by midterm period. e. Calculate the probability that there will be a failing student within the first semester. F. Calculate the probability that a failing student will be first spotted after midterm up to end of the first semester?

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