In an acid-base titration, a base or acid is gradually added to the other until they have completely neutralized each other. Let Xand Y denote the milliliters of acid and base needed for equivalence, respectively. Assume X and Y have a bivariate normaldistribution with ox = 5 mL, oy = 2 mL, μx = 120 mL, y = 100 mL, and p = 0.6.Determine the following:(a) Covariance between X and Y.(b) Mean and standard deviation of marginal probability distribution of X.Mean = imLStandard deviation = iXIY-102(c) P(X < 116) =(d) Mean and variance of conditional probability distribution of X given that Y = 102.HX|Y=102= i= | i(e) P (X < 116 | Y = 102) =mLiRound your answer to three decimal places (e.g. 98.765).mL. Round your answer to two decimal places (e.g. 98.76).mL. Round your answer to two decimal places (e.g. 98.76).Round your answer to three decimal places (e.g. 98.765).Statistical Tables and Charts

Let X denote milliliters of acid and Y denote the milliliters of base.Assume X and Y are bivariate…

Answered: In an acid-base titration, a base or…

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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Let X∼Uniform(0,1) distribution. Find the PDF of Y= 3√X and derive the expected value and the variance of Y.
Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 43 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.50 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit 1 upper limit 2 margin of error 3 (b) What conditions are necessary for your calculations? (Select all that apply.) n is large the distribution of weights is normal σ is known the distribution of weights is uniform σ is unknown (c) Interpret your results in the context of this problem. 1% of the intervals created using…
Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 45 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that o = 7.60 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.) n is large the distribution of weights is normal o is known the distribution of weights is uniform o is unknown (c) Interpret your results in the context of this problem. The probability that this interval contains the true average…
We want to test the relative efficacy of a new cholesterol lowering drug A versus existing drug B. We randomize nĄ subjects with high cholesterol to take treatment A and ng subjects to take treatment B. After a l-month followup, we measure cholesterol levels in both groups. Suppose the data in the two groups are independent and YA,Y;ª,..., YA N(µA, o²) and YB,YB,.., Y,B iid N(µB,0²), where o? = 9 is known. Let Y4 and YB be the sample average cholesterol level in group A and B. 1. What is the distribution of the difference in sample means: Â =Ÿª-ŸB? Hint: what is the distribution of each group's sample average? What do we know about linear combinations of normal RVs? 2. Let A = µA - µB be the true difference in cholesterol levels in populations treated with Â-A A versus B. What is the distribution of Z = ? Vo2/na+o²/ng 3. Suppose YA = 20 and YB = 26 with na = nB = 36. Conduct an a = .05 significance level test of Ho : A = 0 versus Ha : A # 0. Do you reject or fail to reject the null at…
From the following data calculate (i) Correlation coefficient (ü) Standard Deviation of Y (Gy) X=-85 Y Y= 89 X Gz=3
Is there a relationship between (X) rate of poverty (measured as a percent of population below poverty level) and (Y) rates of teen pregnancy (measured per 1,000 females aged 15 to 17)? A researcher selected random states and collected the following data. The correlation coefficient between was 0.98. Determine whether the correlation is significant. Use the correlation test statistics. Compute the appropriate test statistics. The degree of freedom is 6 and alpha at 0.05.
A: 98, 100,93,71,73,79,89,82,82,84,79,71,91,72 B: 15,33,16,40,30,34,31,38,29,28,24 calculate coeffecient of variation,CV,Round to one decimal place.
The data in personalities is bivariate normally distributed Carry out a formal t-test for the association between extroversion and neuroticism in personalities H0: The population correlation coefficient is 0. HA: The population correlation coefficient is not 0. What is the value of the t-statistic corresponding to this test? Carry out a formal t-test for the association between extroversion and neuroticism in personalities. H0: The population correlation coefficient is 0. HA: The population correlation coefficient is not 0. What is the critical value of the t-statistic required to reject the null hypothesis at a confidence level of 0.05
The following information represents chlorine residuals in swimming pool (y) and the testing time (y) in different hours: n = 6, Ey = 8.8, Ey = 18.68, Ex = 42, Ex2 = 364, and Exy = 48.6 The sample correlation coefficient is: -0.6467 - 0.9899 - 0.9088 0.6467
The average height X and weight Y of males in population have a bivariate normal distribution with means µX 1.80 m., µy 90.0 kgs and standard deviations Ox = 0.30 m., oy = 15.3 kgs respectively. The correlation coefficient between X and Y is p= 0.80.
Psi is a measure of compressive strength, or the ability of the material to carry loads and handle compression. The desired concrete psi rating used for sidewalks and residential driveways ranges from 2500psi to 3000psi obtained from mixing cement, stone, and sand in different ratios but with the same amount of water. The summary of the psi's of three (3) such concrete mixes made by three (3) different civil engineering students is given as follows: Mean vector: The variance-covariance matrix: Concrete mix Mean Concrete mix 1 Concrete mix 2 Concrete mix 3 Concrete mix 1 | Concrete mix 2 2700 18 12 2 3000 12 16 3 2400 Concrete mix 3 16 25 Let the random variable Y be the vector of the psi's of concrete mixes obtained by the students, i.e. Y1, denotes the psi of concrete mix made by student 1, Y2 is the psi of concrete mix made by student 2 and Y3 is the psi of concrete mix psi made by student 3. (a) Find (i) the multivariate probability distribution function (pdf) of Y. (ii) the…
Suppose that y, is an independent response variable (i = 1.....n) with mean, such that g(i) = n₁ = X₁B, where g(.) is a link function, X, is a vector of covariates and 3 is a px 1 vector of coefficients. Let the variance of y; be Var (Y) = V(i), where V(.) is a known function and is a scale parameter. Given: Zi= g'(pi) (Yi - Pi) + Ni w₁ = [V (pi) (g'(pi))²]-¹ 8 where g'(μ) = 9(μ) (a) Show that E(Z₁) = X₂B (b) Show that Var (Z₁) = w¹o. (c) Estimate 3 by minimizing Σ, wi( E(Z₁))² with respect to 3. After you found 8, find the Var(8) and E(3). What do you conclude?

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