Let X be a random sample form N(0, e). Find the complete sufficient statistic for e.
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: Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of…
A:
Q: Consider a random variable X that follows a uniform distribution with a= 1 and b = 4 Find the…
A: Answer: From the given data, X follows a uniform distribution, a = 1 and b = 4
Q: At Burnt Mesa Pueblo, in one of the archaeological excavation sites, the artifact density (number of…
A: (a) Let r be the prehistoric artifacts in the 44 liters of sediment. The Poisson distribution would…
Q: Consider the population : {1, 2, 3, 4, 5}, and suppose this population has the uniform distribution.…
A:
Q: Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of…
A: According our policy we can answer only first three subpart for remaining please repost the…
Q: Suppose z is a normal random variable. Find P ( Z < 1.84 ).
A:
Q: Consider a population consisting of value (1, 3, 5) a. Compute the variance of the sampling…
A: Population : 1 , 3 , 5 n = sample size = 2 with replacement
Q: Let X be a normally distributed random variable with finite expectation u and variance o. Let X be…
A:
Q: Let H be the discrete r.v. that represents the number of heads obtained when a fair coin is flipped…
A: Let H be the discrete r.v. that represents the number of heads obtained when a fair coin is flipped…
Q: Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of…
A: Mean: The mean is the sum of observations divided by the number of observations. that is, Mean = x =…
Q: A simple random sample of 18 male students at a university has an average height of 70 inches. The…
A: Sample size(n)=18 sample mean(x¯)=70 Population standard deviation(σ)=2.8 Let's assume α=0.05
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: Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of…
A: (a) Use TI-83 plus Calculator to obtain the values of sample mean and the standard deviation.…
Q: Determine the distribution of X for the following Let X1, X2, ..., X6 be a random sample from X(10)
A:
Q: (a) Explain why the Poisson distribution would be a good choice for the probability distribution of…
A: (a) The random variable r is defined as the number of prehistoric artifacts found in your 48 liters…
Q: Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of…
A: a. Consider that the random variable has defines the hemoglobin count for healthy adult women.
Q: et x be a random variable that represents hemogiobin count ((HC) in grams per 100 mi ters of whole…
A: Given : 15 18 15 20 15 12 15 16 17 11 Sample size (n)=10
Q: sample of size 50 is taken from a continuous uniform random varlable with parameters 1 and 39. What…
A: We know that The pdf of Uniform distribution is f(x) = 1/(b-a) , a<x<b Variance of X =…
Q: In the airline business, "on-time" flight arrival is important for connecting flights and general…
A: We have given two samples- For sample 1- Sample size, n1 = 16 Sample mean, x1-bar = 74.9% Standard…
Q: Consider a population with mean u = 50 and standard deviation o = 4. Let X1,X2, ... ,X10 be a random…
A: Given: Mean μ=50. Standard deviation σ=4 Determine the expected value of Standard deviation using…
Q: You decide to play K number of video games, where K is a Poisson random variable with parameter A.…
A: Given, the number of video games K is a Poisson random variable with parameter λ and the time spend…
Q: Consider the probablility model with sample space {A,B,C} and P(A)=0.5, P(B)=0.4, P(C)=0.1.Then (a)…
A: Given : The sample space given is A,B,C. Here, P(A)=0.5P(B)=0.4P(C)=0.1 If the events A, B and C are…
Q: In the airline business, "on-time" flight arrival is important for connecting flights and general…
A:
Q: A random variable x can have five values: 0, 1, 2, 3, 4, 5. The probability distribution is: x 0…
A:
Q: Indicate the range of values that the random variable X may assume and classify the random variable…
A: Random Variable: In probability theory, a random variable is a variable whose values depend on…
Q: 14. Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable…
A: The random variable y be the annual return for the Vanguard Balanced Index.
Q: Find the CDF of an exponential random variable with mean 1/λ .
A: Solution
Q: According to one study among a certain people group, pregnancy lengths are approximately normally…
A: Let X be the number of premature babies born to these mothers.
Q: A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and…
A: Given that mean = 1.3 , s.d = 0.9 Find
Q: Only a part Let X1∼U(0,1), X2∼U(0,2) and X3∼U(0,3) be independent random variables. (a) Find the…
A: Given that X1∼U(0,1), X2∼U(0,2) and X3∼U(0,3) are independent random variables. Uniform…
Q: Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers…
A: Given sample size, n=10 x : Hemoglobin count in grams per 100 milliliters of whole blood. x…
Q: ii) Find the value of a sample size n, if the fifth percentile of 1(X₁-X)² is 9.39.
A: Given: Random variable x1, x2,,... Xn from normal distribution N(u, σ^2)
Q: Given that balls are drawn without replacement from a box containing 7 white and 3 black balls. Let…
A: Given that balls are drawn without replacement from a box containing 7 white and 3 black balls.
Q: Suppose X. 1 and 2 are three independent normal random variables. X has an expected value Variable…
A: X, Y and Z are independent normal random variable. Information given in the table. Variable X Y…
Q: a) Let's consider the monthly return of the stocks in the fund to be a sample from the population of…
A: According to the answering guidelines, we can answer only three subparts of a question and the rest…
Q: 2. Let X and Y be independent and identically distributed random variables from Uniform(0,1)…
A:
Q: Cars arrive at a tollbooth at a mean rate of 36 cars every 9 minutes according to a Poisson process.…
A: As per our guidelines we can solve first three subpart and rest can be reposted. Solution-: We find,…
Q: The probability that data are entered incorrectly into a field in a database is 0.008. A data entry…
A:
Q: Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of…
A:
Q: X is a Uniform(8, 20) random variable what is Var(X)=
A: We havé to find variance,
Step by step
Solved in 2 steps with 2 images
- From a population of 4 students, a random variable (X) is measured in terms of age and the values of X are 24, 20, 22, 18. Find the sampling distribution where n = 1 Compute for the Variance when n=1Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows. 14 18 15 19 13 11 15 18 15 12 (i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) X = S = (ii) Does this information indicate that the population average HC for this patient is higher than 14? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. О Но: и 3D 14;B Hі: и 14; Hі: и %3D 14 Но: и 14 О Но: и 3D 14;B Hi: и # 14 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since we assume that x has a normal distribution and o is…Suppose you have a sample of 9 observations Y1,...,Y, from a normal population with mean 2 and variance 4. Let Y and S denote the sample mean and sample variance, respectively. What is the distribution of E ( (a) (b) 653 (c) Suppose X1,X2, X3, X4, X5 are independent random variables from a normal population with mean 0 and variance 4. Define S3 = E(X, - X). What is the distribution of 253 + S3?
- Let a be a random variable representing the percentage of protein content for early bloom alfalfa hay. The average percentage protein content of such early bloom alfalfa should be u = 17.2%. A farmer's co-op is thinking of buying a large amount of baled hay but suspects that the hay is from a later summer cutting with lower protein content. A small amount of hay was removed from each bale of a random sample of 50 bales. The average protein content from the samples was determined by a local agricultural college to be -15.8% with a sample standard deviation of S = 5.3%- At a = .05, does this hay have lower average protein content than the early bloom alfalfa?Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information. x 0.336 0.296 0.340 0.248 0.367 0.269 y 3.2 7.5 4.0 8.6 3.1 11.1 (b) Use a 10% level of significance to test the claim that ρ ≠ 0. (Use 2 decimal places.) t critical t ± (d) Find the predicted percentage of strikeouts for a player with an x = 0.288 batting average. (Use 2 decimal places.) %(e) Find a 95% confidence interval for y when x = 0.288. (Use 2 decimal places.) lower limit % upper limit % (f) Use a 10% level of significance to test the claim that β ≠ 0. (Use 2 decimal places.) t critical t ± (g) Find a 95% confidence interval for β and interpret its meaning. (Use 2 decimal places.) lower limit upper limit please show steps and workIn the airline business, "on-time" flight arrival is important for connecting flights and general customer satisfaction. Is there a difference between summer and winter average on-time flight arrivals? Let x1 be a random variable that represents percentage of on-time arrivals at major airports in the summer. Let x2 be a random variable that represents percentage of on-time arrivals at major airports in the winter. A random sample of n1 = 16 major airports showed that x1 = 74.9%, with s1 = 5.3%. A random sample of n2 = 18 major airports showed that x2 = 70.2%, with s2 = 8.6%. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. (a) Does this information indicate a difference (either way) in the population mean percentage of on-time arrivals for summer compared to winter? Use α = 0.05. (i) What is the…
- A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of 8 employees provides the following (refer Table 4): Employees y X1 X2 1 100 9 6 2 90 4 10 3 80 8 9 4 70 5 4 5 60 5 8 6 50 7 5 7 40 2 4 8 30 2 2 (a) Run a regression analysis based on the data in Table 4 using Mic. Office EXCEL. Based on theoutput, propose a regression equation that can be used to predict paralegal GPA.(b) Interpret the coefficient value of each independent variable in the constructedmodel(c) Is each independent variable sharing a significant linear relationship with the dependent variable?Verify at 0.05 level of significance. Make your conclusion based on the p-value in the EXCEL output.A certain type of tree has seedlings randomly dispersed in a large area, with the mean density of seedlings being approximately three per square yard. If the seedlings are randomly dispersed, the number of seedlings per region, Y can be modelled as a Poisson random variable. If a 1 forester randomly locates ten 1-square-yard sampling regions in the area, the probability that none of the regions will contain seedlings is 0.0498. 2.3.1 If the seedlings really are randomly dispersed, the number of seedlings per region, Y, can be modelled as a Poisson random variable with 2 = 3. Interpret 1 =3. 2.3.2 State the moment generating function_of the random variable Y.The weight of a male bald eagle has approximately a normal distribution with mean ?= 7.4 pounds and a standard deviation of ?= 1.6 pounds. Suppose we take a random sample of n=64 male bald eagles. Let X̄ be the random variable representing the mean weight in pounds of the 64 sampled male bald eagles. Let Xtot be the random variable representing sum of the weights of the 84 sampled bald eagles. a) About what proportion of male bald eagles have weights between 7.0 and 7.8 pounds? b) About what proportion of male bald eagles have weights greater than 7.8 pounds? c) About how many of the 64 sampled male bald eagles would you expect to have weight greater than 7.8 pounds? (nearest integer)? d) About how many of the 64 sampled male bald eagles would you expect to have weight between 7.0 and 7.8 pounds? (nearest integer)? e) What is the standard deviation of the distribution of X̄ (in pounds)? f) What is the standard deviation of the distribution of Xtot (in pounds)? g) What is the…
- 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 36 minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that μ is greater than 36 minutes. The consultant plans to do a statistical test and collects a random sample of 50 shopping times at the supermarkets. Suppose that the population of shopping times at the supermarkets has a standard deviation of 16 minutes and that the consultant performs her hypothesis test using the 0.05 level of significance.Suppose X, Y, and Z are three independent normal random variables. X has an expected value of 7 and a standard deviation of 2; Y has an expected value of -2 and a standard deviation of 4; Z has an expected value of 5 and a standard deviation of 12. Let T = 3X + 12Y - 2Z Variable X Y Mean(Expected Value) 7 -2 Standard Deviation 2 4 12 Coefficient 3 12 -2 a) What is the expected value of T? b) What is the variance of Z? c) What is the variance of T? d) What is the standard deviation of T? N LOTotal blood volume (in mi) per body wight (in ke) is important in medical research. For healthy aduks, the red blood cell volume mean is about p = 28 ml/kg.t Red blood cell vokume that is too lom ar too high can indicate a medical problem. Suppose that koger has had seven blood tests, and the red blood cell volumes weré as follows Let x be a random variable that represents Roger's red blood cll volume. Assume that x has a narmal distributian and - 4.75. Do the data indicate that koger's red blood cell valume is different (either way) from a- 28 mi/kg? Use a 0.01 lervel of significance. a What is the leval of sigaicance State the null and alternate hypotheses. Will you use a left-lailed, right-laded, or two-tailed test? O H: - 28 ml/kg; H: 2s m/kg; Ima-tailed o Ho: - 28 ml/ka; H 28 m/ka, let-tailed O Ho: 28 mil/kg: H1:- 28 ml/kg; tmo-tailed O Ho: 28 m/ka, H > 28 m/kg; right-laiked (b) What sampling distribution wil you use? Explain the rationale for your choice of sampling distributian.…
