Here, X is the sample mean of X, ... ,Xp. ( a) Show that Σ(Χ, - X)" Σχ)-ηX? (b) Show that E(E X) = n(µ² + o²) [Hint: E(Y²) = Var(Y) + [E(Y)]².] (c) Show that E (nX²) = nµ² + o². [Hint: Apply the similar relation given in the previous hint]
Q: Suppose that x,, X, ..., X and Y,, Y,, ..., Y, are independent random samples, with the variables x,…
A: Given Xi~ N(μ1,σ12) and Yi~N(μ2,σ22 )
Q: 1.) In a binomial experiment, the probability of success in each trial is 0.45, and 30 trials are…
A: We have given that Number of trials n=30 Success of probability p =0.45 q=1-p X~binomial ( n,p)
Q: If Y1, Y2, ... , Yn denote a random sample from the normal distribution with unknown mean u and…
A:
Q: At another park, at a random selected time, there were 80 individuals having a picnic. It was found…
A: From the provided information, Sample size (n) = 80 40% of them were fully vaccinated that is p =…
Q: A synoptic uses Bernoulli random variable X to describe the weather conditions within one year…
A:
Q: e standard deviation is larger than 110% of the population standard deviation. Correct your answer
A: A random sample is given as, n=22. The mean is , μ=300. The variance is, σ2=255. The probability…
Q: Show that adding a constant K to a random variable increases the average by K but does not change…
A: Suppose I have a below data For random variable X 2,5,8,4 consider k= 2 Average of 2,5,8,4 using…
Q: and second components meet specifications are 0.96 and 0.89, respectively. Let X be the number of…
A: The random variable X defines the number of components in the assembly that meet specification.
Q: Let x be a random variable that represents red blood cell (RBC) count in millions of cells per cubic…
A: Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…
Q: (b) The number of red balls in a sample of 8 balls chosen at random from a box contains 30 balls of…
A: We have to find the mean and variance of Hypergeometric distribution.
Q: Let x1,...x40 be IID binomial random variable with parameters p = 0.3 find the mean and variance of…
A: Let x1,...x40 be IID binomial random variable with parameters p = 0.3 We need to find the mean and…
Q: Assume thAt scores on a standardized test are known to follow a bell shaped distribution with a mean…
A: L
Q: Yoonie is a personnel manager in a large corporation. Each month she must review 10 of the…
A: Given Data: μ=4σ=0.9n=10
Q: Suppose that the random variable X measures the number of hot dogs purchased in a food court in an…
A: CorX,Y=0.75VX=VY=36W=2X+3Y
Q: Suppose that X is a random variable with mean 30 and standard deviation 4. Y is a random variable…
A: The standard deviation of X is 4 and standard deviation of Y is 8.
Q: 3. (18/222, Expected Value and Variance) The Philippine Housing Survey reported the following data…
A: E(X)= ΣXi*fi/Σfi fi represents the renter-occupied houses. E(X)=…
Q: Suppose that "duration of any attempt in an effort to score (X)" by either team in college soccer…
A: Given: Let X be a random variable that represents the duration of any attempt in an effort to score.…
Q: Q2 (a) The heights of a particular species of trees have a normal distribution with mean 2.1m and…
A:
Q: Let x be a random variable that represents red blood cell (RBC) count in millions of cells per cubic…
A: Disclaimer "Since you have posted a question with multiple sub-parts, we will solve first three…
Q: Let X1, X2, X3... X20 be a random sample from a distribution with mean 8 and variance 5. Find the…
A:
Q: A couple wishes to have children until they have exactly two female children in their family. p =…
A: Given problem Given that A couple wishes to have children until they have exactly two female…
Q: A population, T is normally distributed with unknown mean, u and variance 49. A sample of size 9…
A: Given : Population variance (σ2) = 49 Sample size (n) =9 Sample mean (X¯) = 20 Confidence level =…
Q: Let x be a random variable that represents red blood cell (RBC) count in millions of cells per cubic…
A: Hypothesis testing is conducted for the parameters of the population like population mean,…
Q: Probability of getting COVID-19 virus in a community is 0.03. If a sample of three persons are…
A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…
Q: Let X₁, X2, X, be normal random variables with mean and variance 2. What are the method of moments…
A: X~N(μ,σ2)
Q: Yoonie is a personnel manager in a large corporation. Each month she must review 15 of the…
A:
Q: The following table gives the outputs of 3 years for a farm that uses 3 types of fertilizers,…
A: Given: Level of significance = 0.05 x1 x2 x3 year1 10 42 54 year2 22 47 61 year3 28 31…
Q: Carboxyhemoglobin is formed when hemoglobin is exposed to carbon monoxide. Heavy smokers tend to…
A: Part a: From the given data we have: S.No. X x-xbar 1 9.1 2.1025 2 9.8 0.5625 3 10.6…
Q: Yoonie is a personnel manager in a large corporation. Each month she must review 10 of the…
A: a) Define a random variable X, that is the time to review.
Q: We have a random variable Y with unknown mean value. We have obtained a random sample of 10 values…
A: From the provided information, Sample size (n) = 10
Q: Consider two independent random variables X and Y with Means of 17 for the first variable is 1 and…
A: Let the new variable be Z = 3X - 4Y The mean is given by E(Z) =3E(X) - 4E(Y) E(Z) = 3(17) -…
Q: 1. Two samples drawn from normal distributions with the following sample sizes: ni =15 and n:= 15.…
A:
Q: In a customer service center, there are 18 complaints dropped per minute. What is theprobability…
A:
Q: 3. (18/222, Expected Value and Variance) The Philippine Housing Survey reported the following data…
A: E(X)= ΣXi*fi/Σfi fi represents the renter-occupied houses. E(X)=…
Q: The number of traffic accidents on a section of the M4 freeway during peak flow periods follows a…
A: The provided information is as follows:The number of traffic accidents on a section of the M4…
Q: 9. Final: For recent period of 100 years, there were 530 Atlantic hurricanes. Assume the Poisson…
A:
Q: Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female…
A: Assume that the random variable X defines the weight of healthy adult female deer.According to the…
Q: Suppose that x is a normally distributed random variable with mean 5 and standard distribution is 6.…
A:
Q: Consider a random variable X that follows a uniform distribution with a= 3 and b = 8 Find the…
A: Answer: From the given data, A random variable X follows uniform distribution with parameters a = 3…
Q: From the data set of a class, a student taking a final exam is random variable with mean equal to 50…
A:
Q: Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the…
A: The question is about sampling distribution.Given :Population mean time to complete a review ( ) =…
Q: X is a binomial random variable with n= 20 and p= 0.46 Find the mean and variance for X?
A: Answer: Using the given data, X follows binomial distribution with n = 20 and p = 0.46 X ~ Binomial…
Q: Find the value of variance in the Binomial distribution where there are 5 samples and p=0.3.
A: The formula of the variance for binomial distribution is,where,n denotes the sample sizep denotes…
Q: Let x be a random variable that represents the pH of CVS brand water. The mean of this x…
A: Given: μ = 6.5 n = 70 X = 7.2 s = 2.5 α = 0.05 Formula Used: Test-statistic t = X-μsn
Q: Suppose that X1, X2, X3 and X4 are all independent random variables, each with a normal…
A:
Q: Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female…
A: Given Information: Mean (u) = 62 kg Standard Deviation (s) = 9 kg Sample size (n) = 70 Sample…
3. Let X1, … , Xn" be a random sample from a distribution with
![Here, X is the sample mean of X, ... ,Xp.
( a) Show that Σ(Χ, - X)" Σχ)-ηX?
(b) Show that E(E X) = n(µ² + o²) [Hint: E(Y²) = Var(Y) + [E(Y)]².]
(c) Show that E (nX²) = nµ² + o². [Hint: Apply the similar relation given in the previous hint]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd3be9fc5-49dc-4987-93dc-30b0d6519ab7%2F24f8191b-9a5a-4e5a-ae5e-ce74753f1ac2%2Fmebm1hq_processed.png&w=3840&q=75)
Step by step
Solved in 4 steps with 4 images
- Yoonie is a personnel manager in a large corporation. Each month she must review 10 of the employees. From past experience, she has found that the reviews take her approximately 4 hours each to do with a population standard deviation of 1.1 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X¯¯¯ be the random variable representing the mean time to complete the 10 reviews. Assume that the 10 reviews represent a random set of reviews. (a) What is the mean, standard deviation, and sample size? Mean = Standard Deviation = Sample Size = (b) Complete the distributions. Round all decimals to four decimal places. X∼ ( Number, Number) X¯¯¯∼ ( Number, Number)The weight of goods shipped in containers of a certain size is a normally distributed random variable. It is known that 65% of the containers have a net weight above 4,98 tons, and 45% of containers net weight above 5,2 tons. Find the mean and standard deviation of the net weight containers.Let x be a random variable that represents the pH of CVS brand water. The mean of this x distribution is µ = 6.5 pH. A new company wants to sell its water at CVS locations. However, CVS management believes that the new brand will have a mean pH less than the CVS brand water. A random sample of 50 water samples were taken from this new company's water and it was found that the sample mean was 6.3 pH and the sample standard deviation was s = 0.5 pH. Do the data indicate that the new company's water has a mean pH level less than 6.5, which is the pH of the CVS brand water. Use a 5% significance level. Identify the following in your answer. 1. Identify the null Ho and alternative hypotheses H1 for the problem. 2. Identify the following: Sample statistic • Test Statistic (t): (Round to three decimal places) p - value: (Round to four places) • Calculator key used. 3. Identify the significance level and determine if you reject or fail to reject the null hypothesis. 4. State your conclusion.
- An X random variable comes from any distribution with 21 averages and 17 variances. What is the probability that a sample of 45 randomly selected from this stack has a sample mean between 20 and 26? Calculate.Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, μ, spent by customers at the supermarkets has been reported to be 38 minutes, but executives have good reason to believe that u is different from 38 minutes. The executives hire a statistical consultant and ask her to perform a statistical test. To perform her statistical test, the consultant collects a random sample of shopping times at the supermarkets. She computes the mean of these times to be 44 minutes and the standard deviation of the times to be 10 minutes. Based on this information, complete the parts below. (a) what are the null hypothesis Ho and the alternative hypothesis H₁ that should be used for the test? Ho H₁ :0 (b) Suppose that the consultant decides not to reject the null hypothesis. What sort of error might she be making? (Choose one) ▼ (c) Suppose the true mean shopping time spent by customers at the supermarkets is…4. Suppose that 60% of college students own a smart phone manufactured by Apple. If a random sample of 200 college students is selected, use the normal distribution to approximate the probability that the number of students in the sample owning a smartphone made by Apple will be less than 105. Is it reasonable to use the normal approximation here?
- 1. Six batteries taken at random from a large lot were subjected to life tests with the following results: 19, 22, 18, 16, 25, and 20 hours. Find the probability that the sample mean of x= 20 hours, as observed here, or one less than 20 hours could arise if the true mean of the lot of batteries is 21.5 hours, assuming a known variance of o = 10 hours, for the individual batteries in the lot. %3DLet X be a binomial random variable with a mean of 0.5 and a variance of 0.45. Find P(x is greater than or equal to 1)
