A binary message m, where m is equal either to 0 or to 1, is sent over an information channel. Assume that if m = 0, the value s = −1.5 is sent, and if m = 1, the value s = 1.5 is sent. The value received is X, where X = s + E, and E ∼ N(0, 0.66). If X ≤ 0.5, then the receiver concludes that m = 0, and if X > 0.5, then the receiver concludes that m = 1.
If the true message is m = 0, what is the probability of an error, that is, what is the probability that the receiver concludes that m = 1? Round the answer to four decimal places.
If the true message is m = 1, what is the probability of an error, that is, what is the probability that the receiver concludes that m = 0?
A string consisting of 60 1s and 40 0s will be sent. A bit is chosen at random from this string. What is the probability that it will be received correctly?
Refer to part (c). A bit is chosen at random from the received string. Given that this bit is 1, what is the probability that the bit sent was 0?
Refer to part (c). A bit is chosen at random from the received string. Given that this bit is 0, what is the probability that the bit sent was 1?
In: Statistics and Probability
In: Computer Science
Your insurance company has coverage for three types of cars. The annual cost for each type of car can be modeled using Gaussian (Normal) distribution, with the following parameters:
Use the Random number generator and simulate 1000-long columns, for each of the three cases. Example: for the Car Type 1, use Number of variables=1, Number of random numbers=1000, Distribution=Normal, Mean=520 and Standard deviation=110, and leave random Seed empty.
Next, use either sorting to construct the appropriate histogram or rule of thumb to answer the questions:
13. What is approximate probability that Car Type 1 has an annual cost less than $350?
14. Which of the three types of cars is least likely to cost less than $350?
15. For which of the three types we expect that (approximately) 95% of cases will be between $300 and $740?
In: Statistics and Probability
Your insurance company has converage for three types of cars. The annual cost for each type of car can be modeled using Gaussian (Normal) distribution, with the following parameters:
Use the Random number generator and simulate 1000-long columns, for each of the three cases. Example: for the Car Type 1, use Number of variables=1, Number of random numbers=1000, Distribution=Normal, Mean=520 and Standard deviation=110, and leave random Seed empty.
Next, use either sorting to construct the appropriate histogram or rule of thumb to answer the questions:
13. What is approximate probability that Car Type 1 has an annual cost less than $350?
14. Which of the three types of cars is least likely to cost less than $350?
15. For which of the three types we expect that (approximately) 95% of cases will be between $300 and $740?
Task 3
In: Statistics and Probability
The national surveyconducted a poll examining the financial health of public servants as they approach retirement age. According to responses from the survey of persons 55 years of age and over, 60% of them have stated that they are adequately prepared for retirement. Proposed changes to mandatory retirement laws may mean that persons who would normally be retiring at age 65, may no longer choose to do so, particularly if they feel they are not financially in the position to. Based on the findings of this survey, you want to extrapolate the number of people in your division who are adequately prepared for retirement. To do so, a random and independent sample of employees ages 55 plus where n=10 was conducted.
a) Define the random variable x as the number of persons who feel adequately prepared for retirement. We know that x is a binomial random variable. Please write a paragraph explaining what random varioable x means in the given context. Use graphs, number or whatever is required to answer the question. It can be about a page long.
b) Find the probability that more than 5 people who responded are adequately prepared for retirement. This will help you plan for future hiring. Please calculate and also mention the logic and reason behind it while answering. please show each steps in terms of how you calculate what you calculate, for example, variance, standard deviation etc. I am interested in all the formula and steps you use.
In: Statistics and Probability
Isabel Briggs Myers was a pioneer in the study of personality types. The personality types are broadly defined according to four main preferences. Do married couples choose similar or different personality types in their mates? The following data give an indication. Similarities and Differences in a Random Sample of 375 Married Couples Number of Similar Preferences Number of Married Couples All four 29
Three 127
Two 111
One 67
None 41
Suppose that a married couple is selected at random. (a) Use the data to estimate the probability that they will have 0, 1, 2, 3, or 4 personality preferences in common. (For each answer, enter a number. Enter your answers to 2 decimal places.) 0 1 2 3 4
(b) Do the probabilities add up to 1? Why should they? Yes, because they do not cover the entire sample space. No, because they do not cover the entire sample space. Yes, because they cover the entire sample space. No, because they cover the entire sample space.
c. What is the sample space in this problem?
0, 1, 2, 3 personality preferences in common
1, 2, 3, 4 personality preferences in common
0, 1, 2, 3, 4, 5 personality preferences in common
0, 1, 2, 3, 4 personality preferences in common
In: Statistics and Probability
Cars arrive at a parking lot at a rate of 20 per hour. Assume that a Poisson process model is appropriate. Answer the following questions. No derivations are needed but justification of your answers are necessary. What assumptions are necessary to model the arrival of cars as a Poisson process? What is the expected number of cars that arrive between 10:00 a.m and 11:45 a. m? Suppose you walk into the parking lot at 10:15 a.m.; how long, on average, do you have to wait to see a car entering the lot? Assume that the lot opens at 8 a.m. what is the expected time at which the ninth car arrives at the parking lot. What is the expected waiting time between the arrival of the 9th and 10th car? How is the waiting time between the arrival times of 9th and 10th car distributed? Write the density function of the waiting time. As an outsider, you watch the cars entering the parking lot for a half an hour in the morning (between 10 a.m and 10:30 a.m.) and then for a half an hour during the lunch time (between 1 p.m. and 1:30 p.m.). What can you say about the number of cars arriving at the parking lot during the two half hour periods? Suppose the probability that a car will need a handicapped parking spot is 1%, what is the expected number of cars needing handicapped spots between 10:00 am and 11:45 am?
In: Statistics and Probability
Pease answer the questions below:
|
# of Pairs of Shoes |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
Frequency |
7 |
8 |
4 |
11 |
8 |
9 |
8 |
Round all your answers to 4 decimal places where
possible.
The mean is: Incorrect
The median is: Correct
The sample standard deviation is: Incorrect
The first quartile is: Correct
The third quartile is: Correct
What percent of the respondents have at least 6 pairs of Shoes?
Incorrect%
35% of all respondents have fewer than how many pairs of Shoes?
In: Statistics and Probability
Under ordinary circumstances: For all babies born in the entire global population, the proportion of male births tends to be consistently a bit higher, than the proportion of female births (Source: WHO - World Health Organization).
In fact: For a randomly sampled individual birth from the global population, the probability that the baby's sex will be male is approximately 51.22%.
Imagine that we will randomly record the sex outcome at birth for 25 future individual babies from the global population.
We will let random variable X stand for the total number of male births in our sample.
In this scenario, what is the numerical value of E(X)?
Round to one digit past the decimal point, and state just the number part of your answer (no units).
In this same scenario:
What is the numerical value of SD(X)?
Round to one digit past the decimal point, and state just the number part of your answer (no units).
In this same scenario:
What is the approximate value of P(X≤11) ?
Write your answer as a percentage value, and round to three digits after the decimal point. Include a percent symbol after your answer (no spaces).
In this same scenario:
What is the approximate value of P(X>11) ?
Write your answer as a percentage value, and round to three digits after the decimal point. Include a percent symbol after your answer (no spaces).
In: Statistics and Probability
The time between arrivals of parts in a single machine queuing system is uniformly distributed from 1 to 20 minutes (for simplicity round off all times to the nearest whole minute.) The part's processing time is either 8 minutes or 14 minutes. Consider the following case of probability mass function for service times: Prob. of processing (8 min.) = .5, Prob. of processing (14 min.) = .5 Simulate the case, you need to estimate average waiting time in system. Start the system out empty and generate the first arrival time, etc. You need to submit random numbers used (Use the third block of the Random number table to generate interarrival time and the fourth block to generate service time), interarrival time and service time for each part, discuss how you compute (10%) and (you need to generate 20 parts):
(1) clock arrival time for each part (10%),
(2) clock time starts to process each part (10%),
(3) clock departure time for each part (10%),
(4) total waiting time in system for each part (20%),
(5) plot average total waiting time in system versus part number (20%),
(6) plot average idle time of the machine versus part number (compute at the end of each processing) (20%)
In: Statistics and Probability