Let the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3, Find the variance of X.

Compute the mean of Y Compute the mean of X. Compute the variance of X Compute the variance of Y Compute the covariance of X and Y Compute the correlation of X and Y Joint Distribution of Weather Conditions and Commuting Times No Rain (X1) 0.28 0.05 0.33 Long commute (Y=0) Short commute (Y=1) Total Rain (X=0) 0.38 0.29 0.67 E(M)= 0.34 (Round your response to two decimal places) E(X)=0.33 (Round your response to two decimal places) = 2211 (Round your response to four decimal places) 2244 (Round your response to four decimal places) comp ®x*[ ] (Round your response to four decimal places) Total 0.66 0.34 1.00

This cardiologist gets a report on his patients' sugar consumption from the nutritionist. He becomes concerned that his patients seem to consume even more sugar that what is in a typical American diet. He decides to take a random sample of 100 of his patients and calculate the mean sugar consumption, x̅, of these 100 patients. The mean sugar consumption for these 100 patients is 17.3 teaspoons. Let's assume, for the moment, that his patients are no different than the general population of Americans with µ (daily sugar consumption) = 16.1 teaspoons and σ = 3.5 teaspoons and that his sample of 100 patients is one random sample from this population. What is the probability of obtaining a mean sugar consumption of 17.3 teaspoons (or more) in his sample of 100 patients if his patients are similar to the general population? What is the probability that the average (x̅) is greater than 17.3?

Let X1 ∼ N(μ = 2, σ^2 = 4), X2 ∼ N(μ = 1, σ^2 = 16), and X3 ∼N(μ = −4, σ^2 = 9). Let X1, X2, and X3 be independent and Y = (X1 + 2X2 + X3)^2. What is the mean and 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 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 ? = 7.80 ml/kg for the distribution of blood plasma. (d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.00 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.) male firefighters

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 ? = 7.30 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.) ? is unknown n is large the distribution of volumes is uniform the distribution of volumes is normal ? is known     (d) Find the sample size necessary for a 99% confidence level with maximal…

Please selct all that apply and explain why

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The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−3/4. Calculate Var(X+Y) with a full explanation