Suppose random variables X, Y are jointly distributed as f(x,y). Match the following: Sa v Sy F(x, y)dydx Choose. Se Sy Yf(x, y)dydx Choose.. S„(X – Ha)² Sy f (x, y)dydx Choose.

1. Describe the key features of the normal curve and explain why the normal curve in real-life distributions nevermatches the model perfectly.

A researcher that wanted to estimate the expectation AY of a random variable Y got three independent observations, Y, Y, Y The researcher knows the value o, of the variance of Y and is considering the following estimators: Pi = 4) Yi + (+) ¥ Py = () Yn + (;) ¥½ + () Y½ in (}) Yi + (}) ¥z + (() %D Which of the following is correct? ONone of the above Ois an unbiased estimator of l and it has the smallest variance of the three estimators. Ois an unbiased estimator of µ and it has the smallest variance of the three estimators. O and i, are both unbiased estimators of fl and Var (ſîz) < Var (îì3). is an unbiased estimator of µ and it has the smallest variance of the three estimators.

A directional hypothesis test has a critical region that consists of the extreme ends of both the left and right side of the t distribution.   True or false?

'Melanoma' is a form of skin cancer and each year 17% of the patients who suffer from the disease die. A random sample of 10,000 melanoma patients is formed at the start of a year. Let Y denote the number of patients in this sample who will die during the year? (a) What is the expected value of Y? That is, compute E(Y). Answer: [Select] (b) What is the variance of Y? That is, compute var(Y). Answer: [Select] (c) What is the probability that Y exceeds 1,800? That is, compute P(Y> 1,800). Answer: [Select]