The Uniform Distribution

Distributions of Continuous Random Variables

Lecture 10

The West

The South

The Midwest

New England

IV The main industries and cities.

American manufacturing began in the Northeast. The first factories were in New England. They produced cotton cloth, supplied coal, natural gas, oil and water power to other regions.

Fishing has been important in the Northeast. Many towns began as a fishing community: Boston, Portland, New Bedford and Gloucester.

The eastern part of the Midwest is corn country. This region is called the Corn Belt. Farming is the leading industry.

The northern part of the Midwest is a hay and dairy region. Wisconsin is the leading dairy state.

The drier western parts of the Midwest are wheat lands. There is a big supply of raw materials – iron ore, livestock, wheat, timber, etc.

Meat packing and flour milling are big Midwestern business. Buffalo, at the eastern end of Lake Erie in New York State, is a milling centre. It is cheaper to transport goods by water than by rail.

Detroit is the centre of automobile industry. Over half the motor vehicles and equipment made in the USA comes from the Midwest.

The South is rich in natural resources: sulphur, salt, phosphate, natural gas, iron ore, coal. Birmingham is an important producer of iron and steel. Oil and natural gas help refinery and chemical industry to develop in the South.

The three states of the West Coast – California, Oregon and Washington – have important farm lands. The crops in California are cotton, wheat, rice and barley. Los Angeles is famous for its oil, aircraft and tire manufacturing, automobile assembly plants.

Another West Coast manufacturing centre is the San Francisco Bay area with its food processing, oil refining and electronics.

Answer the questions:

1. What are the main physiographic divisions of the US?

2. Name the main mountain ranges, the highest peaks and the lowest points in the US.

3. What are the major rivers and lakes of the USA?

4. How does the climate vary throughout the country?

5. What natural resources are found in the USA?

6. Can you remember the most important cities and industries developed in the US?

Continuous random variables that appear to have equally likely outcomes over their range of possible values possess a uniform probability distribution, perhaps the simplest of all continuous probability distributions.

Figure Assigning probabilities for generating a random number between 0 and 1. The probability of any interval of numbers is the area above the interval and under the curve.

Suppose the random variable x can assume values only in an interval . The height of is constant in that interval and equals 1/(d-c). Therefore, the total area under is given by

Total area of rectangle =(Base)(Height)

=

Probability Distribution, Mean, and Standard Deviation of a Uniform Random Variable x

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