Cold War2 essays

Cold War2 essays The Cold War never presented any real threat on America. It was nothing more than the propaganda of two battling super powers. The two super powers involved in the Cold War were The United States of America and The Soviet Union. The two countries were constantly battling over who is the most powerful on the planet. The supposed threats were mere techniques of propaganda used to scare the other countries public into believing they were more powerful. Over and over again the U.S would flex its muscles and then The Soviet Union would flex its muscles until eventually one country couldnt. The Cold War lasted a very long time and it was fought through battles such as the Korean War and Vietnam. Each battle split the country and the U.S would take a side and The Soviet Union would take a side and they would use the country as a battle ground. This was the only actual fighting that occurred. The Cuban missile crisis was an important event that took place during the cold war. In the Cuban missile crisis, America was fearing that The Soviet Union had certain missile instalations in Cuba . The U.S found out about these missile installments from satellite imagery that showed the missiles being transported to Cuba and show the missile sites inside Cuba. "With Castro's approval, the Soviet Union began building secret missile bases in Cuba. On October 16, President Kennedy was shown photographs of the missile installations in Cuba." (Rawnsley, 7) On the surface one would get scared by something like this and that is exactly what The Soviet Union wanted to happen. The whole Cold war was propaganda so by scaring the U.S into thinking they had missiles in Cuba gave them the edge on the war. If The Soviet Union wanted to bomb the U.S they could have easily snuck the missiles in and hidden them. They knew about the satellites and purposely exposed the missiles. "A naval blocka de was imposedosed on Cuba to stop the cons...

Understanding Relative Frequency Histograms

Understanding Relative Frequency Histograms In statistics, there are many terms that have subtle distinctions between them. One example of this is the difference between frequency and relative frequency. Although there are many uses for relative frequencies, there is one in particular that involves a relative frequency histogram. This is a type of graph that has connections to other topics in statistics and mathematical statistics. Definition Histograms are statistical graphs that look like bar graphs. Typically, however, the term histogram is reserved for quantitative variables. The horizontal axis of a histogram is a number line containing classes or bins of uniform length. These bins are intervals of a number line where data can fall and can consist of a single number (typically for discrete data sets that are relatively small) or a range of values (for larger discrete data sets and continuous data). For example, we may be interested in considering the distribution of scores on a 50 point quiz for a class of students. One possible way to construct the bins would be to have a different bin for every 10 points. The vertical axis of a histogram represents the count or frequency that a data value occurs in each of the bins. The higher the bar is, the more data values fall into this range of bin values. To return to our example, if we there are five students who scored more than 40 points on the quiz, then the bar corresponding to the 40 to 50 bin will be five units high. Frequency Histogram Comparison A relative frequency histogram is a minor modification of a typical frequency histogram. Rather than using a vertical axis for the count of data values that fall into a given bin, we use this axis to represent the overall proportion of data values that fall into this bin. Since 100% 1, all bars must have a height from 0 to 1. Furthermore, the heights of all of the bars in our relative frequency histogram must sum to 1. Thus, in the running example that we have been looking at, suppose that there are 25 students in our class and five have scored more than 40 points. Rather than constructing a bar of height five for this bin, we would have a bar of height 5/25 0.2. Comparing a histogram to a relative frequency histogram, each with the same bins, we will notice something. The overall shape of the histograms will be identical. A relative frequency histogram does not emphasize the overall counts in each bin.  Instead, this type of graph focuses on how the number of data values in the bin relates to the other bins.  The way that it shows this relationship is by percentages of the total number of data values. Probability Mass Functions We may wonder what the point is in defining a relative frequency histogram. One key application pertains to discrete random variables where our bins are of width one and are centered about each nonnegative integer. In this case, we can define a piecewise function with values corresponding to the vertical heights of the bars in our relative frequency histogram. This type of function is called a probability mass function. The reason for constructing the function in this way is that the curve that is defined by the function has a direct connection to probability. The area underneath the curve from the values a to b is the probability that the random variable has a value from a to b. The connection between probability and area under the curve is one that shows up repeatedly in mathematical statistics. Using a probability mass function to model a relative frequency histogram is another such connection.