Let S be a continuous random variable representing the students' study time (in hours) fortheir Statistics final paper. The probability density function is given by:= {(2 + + 54s15f(s) =i) Calculate the expected value of S.ii) Calculate the variance of S.iii) Determine E (1145 - 7S - 6S²).,1 ≤s≤4, otherwise

Here given, Let S be a continuous random variable representing the students' study time (in hours)…

Answered: i) Calculate the expected value of S.…

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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8. Let y be a normal random variable with a constant mean E(y) = 4, constant variance var(y.) = o², and a covariance cov(y, y;) = 0 for t# j. Consider the sample mean j = E %3D A. Show that the variance of the sample mean y is .
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 48 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 = 7.10 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 largethe distribution of weights is uniformσ is knownthe distribution of weights is normalσ is unknown (c) Interpret your results in the context of this problem. We are 99% confident that the true…
Y1=X1-3*X2+X3
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 44 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 = 7.40 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.) O the distribution of volumes is uniform O the distribution of volumes is normal O o is unknown O n is large O o is known (c) Interpret your results in the context of this problem. O we are 99% confident that the true average blood…
4. Let X be a random variable and c and d two real constants. Without recurring to variance properties, and knowing that exists X's average and variance, determine the variance of cX + d.
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If E denotes the expectation the variance of a (random variable X is denoted as (E(X))^2 - E(X False a O True .b O
3.Find the population variance or covariance given each scenario below:
Each day a random number, N ,of visitors make a purchase. The mean of N is E(N) = 12.8 and its variance is V(N) = 8.5 %3| Each of these visitors independently from the others spends a random amount of money, X; with mean E(X;)= 130.0 and variance V(X;) = 42.0 Let Y Σ Χ a day. be the total amount of money spent by visitors in the shop in Find the mean of Y and the variance of Y
Consider an estimator of μ: W= 1/6 Y1+1/16Y2+1/4Y3+1/8Y4+1/2Y5 This is an example of a weighted average of the Yi's. Show that W is also an unbiased estimator of μ. Find the variance of W.
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 40 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 = 7.40 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 limitupper limitmargin of error (b) What conditions are necessary for your calculations? (Select all that apply.) n is largeσ is knownσ is unknownthe distribution of weights is uniformthe distribution of weights is normal (c) Interpret your results in the context of this problem. We are 99% confident that the true average blood plasma…
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 40 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 = 7.00 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.) a) σ is known b)the distribution of weights is uniform c)n is large d)the distribution of weights is normalσ is unknown (c) Interpret your results in the context of this problem. a)99% of the intervals…

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i) Calculate the expected value of S. ii) Calculate the variance of S. iii) Determine E (1145 - 7S - 6S²).