代写STAT 400, Spring 2024 Homework 08代做Processing

日期：2024-03-24 05:01

Homework 08

Due Tuesday, March 19, 11:59pm

STAT 400, Spring 2024

Each Exercise or lettered part of an Exercise is worth 5 points. Homework assignments are worth 50 points.

Exercise 1

A certain raw material is classified by its moisture content X (in percent) and impurity Y (in percent). Let X and Y have the joint pmff (x, y) given by

(a) Find the marginal pmf’s for X and Y, their means, and their variances. You may give the marginal pmf’s by either writing them each as a piecewise function or as a table.

(b) Find the covariance and the correlation coefficient of X and Y. 

Exercise 2

In Pawnee, Indiana, the price of a pound of bacon (X) varies from day today according to a Normal distribution with mean of $4.10 and a standard deviation of $0.16. The price of a dozen eggs (Y) also varies from day today according to a Normal distribution with a mean of $1.90 and a standard deviation $0.06. Assume the prices for a pound of bacon and a dozen eggs are independent.

(a) Find the probability that on a given day, the price of a pound of bacon is more than twice as expensive as a dozen eggs. That is, find P(X > 2Y).

(b) Ron wants to cook breakfast for himself, so he buys 10 pounds of bacon and 6 dozen eggs. Find the probability that he paid more than $50 for the bacon and eggs.

Exercise 3

The Illinois Student Senate wants to know the mean amount of money spent by Illinois students for textbooks this semester. Suppose the population mean based on past data over the past few years is $450 and the population standard deviation is $40.A random sample    of 625 students is taken.

(a) What is the probability that the sample mean will be less than $453?

(b) What is the probability that the sample mean will be within $3 of $450? That is, what is the probability that the sample mean will be between $447 and $453?

(c) What is the probability that the sample mean will be within $10 of $450? That is, what is the probability that the sample mean will be between $440 and $460? 

Exercise 4

An economist wishes to estimate the average family income in a certain population. The population standard deviation is known to be $4,800, and the economist uses a random sample of 225 families. What is the probability that the sample mean will fall within $600 of the population mean?

Exercise 5

Traffic accidents at a particular intersection in Campustown follow a Poisson distribution with an average rate of 1.4 per week.

(a) Find the exact calculation using the Poisson distribution for the probability that there would be exactly 70 accidents at this intersection in one year (i.e., 52 weeks).

(b) Find an approximation using the Normal distribution for the probability that there would be exactly 70 accidents at this intersection in one year (i.e., 52 weeks).