4. Let Y₁, Y2,..., Yn be a random sample of size 5 from a normal population with mean 0 and variance 1. Also let 1.5 Y = = Σ Y₁. Let Y₁ be another independent observation from the population. Determine the distribution of the 5=1 following: ΣΥ. = ĹY?². i=1 (a) W = 5 (b) U = 2 (Y₁-Y)². i=1 (c) R = √5Y6 √W _ 2 (5Ÿ² + Y²) U (d) V=

roblem 1 If the population parameters are μ = 7 and σ = 1: a) Compute the z score for the lowest (x-4) and highest grade (x=10). (15 pts) -3 b) Compute the proportion of the normal distribution corresponds to z-score values greater than the highest grade. (10 pts) 7 = 7 0 σ = I X = 10 3 3.00

Which of the following statement is INCORRECT? If Y, follows the standard normal distribution and Y, follows a chis-square distribution with degrees of freedom n, then nY/Y t distribution. If X1,.., Xn is a random sample from a normal population with population mean 1 and variance 1, then (X -1) + (X - 1 (X, - 1) follows a chi-square distribution with degrees of freedom n. If X,..., Xn is a random sample from a normal distribution with population mean 0 and a known variance o, then must follow a distribution, where X denotes the sample mean and S denotes the sample standard deviation. If T follows at distribution with degrees of freedom n, then T must follow an F distribution with degrees of freedom 1 and n.