2. An analyst wished to gauge the contrast between the extent of clients of two

shampoos who are happy with the prodcut. In an example of 400 clients of Shampoo A

taken by this specialist, 78 said they are satisifed. In another example of 500 clients of

Cleanser B taken by a similar analyst, 92 said they were fulfilled.

a) Construct a 90% certainty stretch for the genuine distinction between the two populace

extents.

b) Based on your answer in (a), what might be your reaction at "=0.1 to the case that

there is no distinction in consumer loyalty between the two shampoos?

3. An overview as of late announced that the mean public yearly consumption for inpatient and

outpatient administrations of all people more than 64 years old was $5,423 with a norm

deviation of $979. An irregular example of 352 people over age 64 living in Sudbury had an

normal cost of $5,516.

a) Can we presume that the mean inpatient and outpatient cost of all Sudbury

inhabitants over age 64 is higher than the public normal of $5,423? Utilize the .01

level of importance.

b) Calculate the P-an incentive for this test. Would your answer have changed on the off chance that you had utilized a

.05 degree of importance?

4.10 Suppose you are given random variables x and y such that x ~ N(Ur, Ox) ylx ~ N(Bo + Bix, 02) so you have the marginal distribution of x and the conditional distribu- tion of y given x. The joint distribution of (x, y) is bivariate normal. Find the 5 parameters (Ux, My, Ox, Oy, Pry ) of the bivariate normal.Problem 1. Let (X, Y) be bivariate normal with /1 = /2 = 0, 01 = 02 = 1, and p = -2. Introduce new random variables U and V which are each a linear combination of X and Y (hence also bivariate normal, ) by U = X - Y, V = X + cy. For what choice of the constant c will U and V be independent? Explain your answer.Let X and Y be two standard normal random variables such that they have a bivariate normal distribution. Further assume that p(X, Y) = 0. Define U = (X + Y)/v2 and V = (X - Y)/v2. (a) Show that U and V are also standard normal and have a bivariate normal distribution. (b) Are U and V independent?2. Let (X, Y) be bivariate continuous random variables with joint PDF f(x, y) - Closetays4 on the set a, y e (0, 412. (i) Calculate C