2. In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. The total waiting time Y in minutes can be shown to have the following PDF 0sy<5 25 f(Y = y) = {2 1 5 25 5sys 10 otherwise a. What is the probability that total waiting time is at most 8 min? b. What is the probability that total waiting time is either less than 2 min or more than 6 min? c. What is the expected total waiting time for the professor? d. Determine the standard deviation in the total waiting time.

2. In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. The total waiting time Y in minutes can be shown to have the following PDF 0sy<5 25 f(Y = y) = {2 1 5 25 5sys 10 otherwise a. What is the probability that total waiting time is at most 8 min? b. What is the probability that total waiting time is either less than 2 min or more than 6 min? c. What is the expected total waiting time for the professor? d. Determine the standard deviation in the total waiting time.

Name: 2. In commuting to work, a professor must first get on a bus near her
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: 2. In commuting to work, a professor must first get on a bus near her house and then transfer to asecond bus. The total waiting time Y in minutes can be shown to have the following PDF0sy<525f(Y = y) = {2 15 255sys 10otherwisea. What is the probabil

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...

See similar textbooks

Related questions

Q: As6. The variance of any processor in a scaled state; Prove that it is the smallest of the…

Q: The results of a mathematics exam at JUST university for two cla Class 1: (n=32, mean=15.7, SD=8)…

A: Given,n1=32 , μ1=15.7 , σ1=8n2=36 , μ2=4.5 , σ2=12α=1-0.95=0.05α2=0.025Z0.025=1.96

Q: =x²³x²+x your answer to 2 decimal places. * Find the mean value of y = Over the range - 1<x<1, and…

A: To find the mean value of given function

Q: The failure time (T) of an electronic circuit board follows exponentially distribution with…

A: As per bartleby policy, I have solved only three sub parts. Please upload the remaining under…

Q: Workers at a large toxic cleanup project are concerned that their white blood cell counts may have…

A: a) Central Limit Theorem: The sampling distribution of sample mean follows normal distribution with…

Q: There is a test designed to measure overall life happiness, (where higher scores indicate more…

A: Given, μ = 85σ = 12 Higher scores indicate more happiness. To find: a. Person with lowest…

Q: Suppose the relationship between Y and X is given by: Y = 1million + 56.43*X + error By how much…

A: The objective of the question is to find out the change in the expected value of Y when X increases…

Q: »51. If x, and x, bé 2 values of a variable x and each of the remaining (n-2) values be (x +x. find…

Q: suppose that a weather station has four electronic wind gauges an gauges an orginal and three backup…

Q: Statistics and Probability In a M/M/1 model, the average number of customers in the system is 6, and…

A: Given information is ; Number of customers in the system (Ls)=6 Average waiting time in the queue…

Q: The mean number of patients admitted per day to the emergency room of a small hospital is 0.5. If,…

Q: 7. Stress levels (measured by cortisol volume) in a certain population are normally distributed and…

A: Given values, μ=200σ=24n=9x¯=180

Q: 2Y 0 Show that has a x² distribution with 2 degrees of freedom.

A: Mean =θ ,

Q: Batman drove from McDonald's to Wendy's on his new riding lawnmower. His average speed was 5 miles…

A: Mean Value theorem. If a function f(x) is continues in an interval x = [a,b] , and differentiable…

Q: We wish to demonstrate that the average time to graduate from Tulane is affected by the students…

A: Claim : students who have taken AP calculus in high school graduate an average of more than 0.25…

Q: (b) On an average 48 trains arrive at the platform of a railway station per day. The stoppage period…

A: Note: Since we only answer up to 3 subparts, we'll answer the first 3. Please resubmit the question…

Q: The 3-point shooter star of your favourite team usually attempts six 3-point shots in a basketball…

A: From the provided information, Sample size (n) = 6 The team record shows that the shooter makes 25%…

Q: If: y = ax² + bx³ where a = 13 and b = 5, find the mean value of y for X between 1 and 3

A: Given :y=ax2+bx3a=13 and b=5

Q: QI/ Four engineering classes A, B, C and, D were tested for the percentage of students success in…

A: Suppose an event happened m number of times out of total n times. Then, the percentage of the event…

Q: 2, Suppose that GMAT final excm grades loge class ormally distelou ted with a mean of 65 and miniman…

A: Given that, μ=65,σ=10 Consider that student must have in order to be in the top 5% of the class. The…

Q: Suppose that X1, X2,... Xn are n values of a variable X and X is the arithmetic mean. Can we obtain…

Q: If the probability of having a boy at birth is 50%. Find the probability that in 40 births there…

A: Given that Population proportion p=0.50 Sample size n =40

Q: The time to failure (in hours) for a laser in a cytometry machine is modeled by an exponential…

Q: The percent of persons (ages five and older) in each state who speak a language at home other than…

A: From the provided information, The probability distribution function of exponential distribution…

Q: The failure time (T) of an electronic circuit board follows exponentially distribution with failure…

Q: The probability that you will get an A grade in Quantitative methods is 0.7.The probability that you…

Q: Suppose that the length of a phone call in minutes follows exponential distribution with parameter…

Q: all students who picked up all the tests they completed prior to taking the final exam. Suppose…

A: Given,Sample 1 :sample size (n1) = 56sample mean (x̄1) = 83sample standard deviation (s1) = 10.4…

Q: . what percentage of females will be forced to look for new pa

Q: The cost of all maintenance for a car during its first year is approximately exponentially…

A: f(x) = λe-λx , x >0 ====================== NOTE: As per the guidelines, I can solve only the…

Q: A researcher believes at 49% of people who grew up as the only child have an IQ score over 100.…

A: Given: Population proportion of people with IQ score over 100 is 50%; P=0.5 Sample size n=400

Q: A sample of n=8 scores has a mean of M=12. If one person with a score of X=9 is removed from the…

A: Given, n=8 Mean (M)=12 Now, M=∑i=18Xin12=∑i=18Xi8∑Xii=18=96

Q: A population with u = 45 and o = 10 is standardized to create a new distribution withu= 100 and o =…

Q: The value for x2 will have an upper tail area of 0.05. There are k = 3 populations and k - 1 = 2…

A: From the provided information, Degree of freedom = k – 1 = 3 – 1 = 2 Level of significance (α) =…

Q: Q.2: Mr. Ahmed is planning to recruit some additional sales staff for his company Al Khalif LLC.…

Q: The cost of all maintenance for a car during its first year is approximately exponentially…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: A five years Business Informatics student studying at TU Wien does some temporary substitute work on…

A: To calculate the mean annual income of the student, we need to build a queuing model. The model will…

Q: 1 b) For any data set, approximately 95% of the observations fall in the interval (T − 2s, T+2s).…

Q: A population has a mean of u = 50 and a standard deviation of a = 10. If 3 points were added to…

A: A population has:Mean=50Standard deviation=10

Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Topic Video

Question

2. In commuting to work, a professor must first get on a bus near her house and then transfer to a
second bus. The total waiting time Y in minutes can be shown to have the following PDF
0sy<5
25
f(Y = y) = {2 1
5 25
5sys 10
otherwise
a. What is the probability that total waiting time is at most 8 min?
b. What is the probability that total waiting time is either less than 2 min or more than 6 min?
c. What is the expected total waiting time for the professor?
d. Determine the standard deviation in the total waiting time.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Discrete Probability Distributions$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

The distribution of the time until a Web site changes is important to Web crawlers that search engines use to maintain current information about Web sites. The distribution of the time until change (in days) of a Web site is approximated in the following table. Days until Probability Changes 1.5 0.05 0.25 0.35 0.20 0.15 3 4.5 7 Calculate the probability mass function of the days until change. *Answers should be in rational numbers with 2 decimal places.
b. The lifetime X of a particular species is assumed to be exponentially distributed with mean 75 time units. Find the probability that a member of this particular species picked at random survives: i. more than 90 time units; less than 70 time units; between 70 and 85 time units. ii. iii. iv. Calculate Var(X).
Let Y be an exponential random variable with (unknown) mean 0.
A bone mineral density test is used to identify a bone disease. The result of a bone density test is commonly measured as a z-score. If the mean bone density test score is found for 9 randomly selected subjects, find the probability that the mean is greater than 0.50. (Round your answer to four decimal points and write in 0.XXXX format.)
Help me please
If the duration of a disease is long and the incidence of the disease is low, the prevalence rate of that disease will be similar to the incidence rate of that disease. True False
1.40 Continuous or Discrete? Identify each variable as continuous or discrete: EX a. Number of homicides in Detroit during a one-month period b. Length of time between arrivals at an outpatient clinic c. Number of typing errors on a page of manuscript d. Number of defective lightbulbs in a package containing four bulbs e. Time required to finish an examination
Today, the waves are crashing onto the beach every 5.1 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.1 seconds. Round to 4 decimal places where possible. The probability that a person will be born between weeks 18 and 52 is P(18<x<52)P(18<x<52) = The probability that a person will be born after week 40 is P(x > 40) = P(x > 10 | x < 47) =
Search and Rescue of DND provides various statistics on boating accidents in he Maritimes and B.C. These statistics include information on the wind speed at the time of the accident. The following chart includes information recorded for 184 accidents on both coasts for the same time period: Wind Conditions Accidents West Coast Accidents East Coast Nil 13 6 Light 74 42 Moderate 30 15 Strong or higher 3 1 a) Suppose xe indicates the wind conditions in the East Coast where xe=0 indicates Nil, xe=1 indicates Light, xe = 2 indicates moderate and xe = 3 indicates Strong or Storm. Also suppose that xw indicates the wind conditions on the West Coast and xt indicates…
Please answer the question in the photo! thanks!
6. True or False? Assume the below life table was constructed from following individuals who were diagnosed with slow-progressing form of prostate cancer and decided not to receive treatment of any form. The calculated survival probability for year 3, if the Kaplan-Meir approach is used to calculate the survival probability, is approximately 0.7438. Time in years Number at risk Nt Number of deaths, Dt Number of censored Ct Survival Probability 0 20 1 1 20 3 2 17 1 3 16 2 1
If I had a series of data X = (x₁+x₂+x₂+ 1 2 +xN} I would have a mean and standard deviation, and s X If I subtracted 3 from every observation in the data series, X, which of the following would happen? The mean of X will increase by 3 The mean of X will decrease by 3 The standard deviation of X will be three times as large The standard deviation of X will be one third as large 3 ...