### Sequence of distinct points converges

Assignment Help Basic Statistics
##### Reference no: EM13990644

1. (a) Let Q be the set of rational numbers. Show that the Riemann integral of 1Q from 0 to 1 is undefined (the net in its definition does not converge). (Q is countable and [0, 1] is uncountable, so the integral "should be" 0, and will be for the Lebesgue integral, to be defined in Chapter 3.)

(b) Show that for a sequence 1F (n) of indicator functions of finite sets F (n) converging pointwise to 1Q, the Riemann integral of 1F (n) is 0 for each n.

2. Let X be an infinite set. Let T consist of the empty set and all complements of finite subsets of X . Show that T is a topology in which every singleton {x} is closed, but T is not metrizable. Hint: A sequence of distinct points converges to every point.

#### Proportion of voters which has changed

After the presidential debates, a random sample of 1200 voters showed that 540 favored the Democratic candidate; 480 were in favor of the Republican candidate; 40 were in fa

#### Educators that students with serum cholesterol levels

Concern was expressed by the health educators that students with serum cholesterol levels above 200 might be at an increased risk of heart disease. If the campus was equally

#### Standard deviation of normal distribution

Suppose 94 percent of the items have lives exceeding 2000 h and 3.51 percent have lives exceeding 16,240 h. Find the mean and standard deviation of the service life.

#### Due to financial hardship

Due to financial hardship, the Nyke shoe company feels they only need to make one size of shoes, regardless of gender or height. They have collected data on gender, shoe size.

#### Information about completing the square

A farmer has 40m of fencing with which to enclose a rectangular pen.Given that the pen is x m wide - show that it's area is (20x - x^2)m^2 and deduce that the maximum area t

#### What was the average speed of bus for entire trip

The bus averaged 40 mph on the drive from Columbus to Athens but averaged 60 mph during the return trip. What was the average speed of the bus for the entire trip?

#### Calculate the risk of breast cancer for women

Calculate the risk of breast cancer for women who were under 25 years old when they had their first child.- Calculate the risk of breast cancer for women who were 25 or older

#### How are confidence intervals calculated

A 95% confidence interval is not so much a statement about any particular interval, such as (79.3, 80.7), but pertains to what would happen if a very large number of like in