How Funds Transfer Pricing (FTP) Is Applied To Measure Bank Profitability - Essay Example

 Math Portfolio Probability Probability is the measure of the likelihood of an event happening. In this paper, I use a problem to perform an experiment that involves probability. Assume that a spinner has four equal parts colored white, black, blue, and green. What would be the chances of landing on white after spinning the spinner? What are the chances of landing on green? The solution for the above problems is 1 in 4 or a quarter. That is, the chances of landing on white is ¼ while the chances of landing on green is equally ¼. In the above problem, the experiment is the spinning of the spinner. The possible outcomes are landing on white, black, blue, and green. One event of this experiment is landing on white. The probability of landing on white is one fourth. The general formula for determining the probability of an event is P (A) = (Number of ways an event can occur/ Total number of possible outcomes). Conditional and Converse Statement A conditional statement is a logical statement that has two parts, that is, a hypothesis and a conclusion. Conditional statements take the form of if ‘p’ (hypothesis), then ‘q’ (conclusion). Contrary, converse statements take the form of; if ‘q’ (conclusion), then ‘p’ (hypothesis). Consider the following conditional statement; if it is raining outside, then it must be cloudy. In this case, ‘raining outside’ is the hypothesis while ‘it must be cloudy’ is the conclusion. The converse statement for the above conditional statement would be, if it is cloudy, then it must be raining outside. If a converse and conditional are true, then one can write a bi-conditional statement. For instance, a conditional statement would be, if two lines intersect to form a right angle, then they are perpendicular. The converse statement would be; if two lines are perpendicular, then they intersect to form a right angle. The bi-conditional statement would be; two lines are perpendicular if and only if they intersect to form a right angle. Syllogism Syllogism is a form of reasoning that draws conclusions from two premises that share a term with the conclusion, and shares other terms that are not in the conclusion. Below is an example of a syllogism. If you want to drive a car, then you need to have a driver’s license. If you need a driver’s license, then you need to go to a driving school. If you need to go to a driving school, then you must have a national identification card. If you need a national identification card, then you must be over 18 years. Applying the law of syllogism for the above example: if you want to drive a car, then you must be over 18 years. Cause and Effect A cause of something is what happens first while the effect is the resulting outcome of the happening. For instance, from the article World War II, the cause of World War II was Germany’s invasion of Poland. The effect was the outbreak of World War II. Normally, there may be many causes for one effect. For instance, flu can be caused by exposure to cold or exposure to allergic substances such as pollen grains. Similarly, one cause can result in many effects. For instance, an El Nino can lead to destruction of crops, death of people or food shortage. The use of Z- score The Z-score is a useful statistic that facilitates the calculation of a score occurring within a given normal distribution. Additionally, the Z-score enables mathematicians to compare two scores selected from different normal distributions. The Z-score converts scores in a normal distribution to Z-scores to give a standard normal distribution. The Z-score is useful in decision-making. Consider the following real life example:  A tutor sets a piece of English Literature coursework for the 50 students in his class. Assuming the scores are presented on a histogram, the data is found to be normally distributed. The mean score is 60 out of 100 and the standard deviation is 15 marks. The tutor has a dilemma. In the next academic year, he must choose which of his students have performed well enough to be entered into an advanced English Literature class. The Z-score can be used to solve the tutor’s dilemma. The Z-score is calculated by: Z = (x-µ)/λ where µ-mean, x-score, λ-standard deviation. Correlation Correlation refers to the relationship between two variables. The correlation range lies between -1 and +1. Results that are near -1 indicate a negative correlation meaning that one value decreases as the other increases. On the other hand, results near +1 indicate a positive correlation, which indicates that the values increase together. An example of correlation would be the relationship between daily temperature levels and daily ice cream sales. An increase in temperature leads to more ice cream sales showing that there is a positive correlation between temperature levels and ice cream sales. The table below indicates the relationship. Temperature (Celsius) Ice cream sales (dollars) 14.3 200 14.7 215 15 250 15.4 275 15.9 300 Cosine Curve/Amplitudes and Periods A cosine curve is a curve whose Cartesian coordinates’ equation takes the form of y=a cos x. The amplitude is a measure of a wave’s height. Since the height of a wave constantly changes, amplitude refers to the farthest distance that the wave gets from its center. In a graph of f (x) = sin x, the wave is centered at the x-axis and the farthest it gets from the axis is 1 unit. The period of a trigonometric function is the horizontal distance traversed before the y-values begin to repeat. The period for y= cos x and y= sin x graphs is 2Π. Amplitude and a period combine to form a cosine curve. Exponential Decay Some things get smaller exponentially. For instance, atmospheric pressure decreases with an increase in altitude. Atmospheric pressure decreases by approximately 12% for every 1000m. This is an exponential decay. The formula for exponential decay is y (t) = a * ekt. The pressure at sea level is around 1013 hPa. With this information, we can calculate the pressure at the top of Mount Everest, which 8848m above sea level. Given the formula y (t) = a x ekt where y (t) is the value at time t, a is the value at start and k is the rate of decay; a = 1013 hPa (pressure at sea level), t is in meters and y (1000) is a 12% reduction in hPa = 891.44 hPa. So 891.44 = 1013 ek*1000 Dividing both sides by 1013: 0.88 = e1000k Introducing logarithms ln (0.88) = ln (e1000k) K= ln (0.88)/ 1000 Therefore, y (t) = 1013 e {ln (0.88)/1000}*t Y (8848) = 1013 e {ln (0.88)/1000)*8848 = 327 hPa. In fact, the pressures at Mount Everest are around 337 hPa. Exponential Growth Some things grow exponentially. Take for example that 2 months ago you had three rabbits. Assuming a constant growth, how many rabbits would you have 2 months from now? Given the formula y (t) = a x ekt where y (t) is the value at time t, a is the value at start and k is the rate of growth; Then 18=3*e2k Dividing both sides by 3: 6 = e2k Introducing natural logarithms: ln (6) = ln (e2k) Therefore, ln (6) = 2k and k = ln (6)/2 In two months’ time the number of rabbits will be: Y (4) = 3 e {ln (6)/2}*4 = 108 rabbits. References "2.5: Amplitude, Period and Frequency. “Amplitude, Period and Frequency. Web. 16 Jan. 2015. . Top of Form Bottom of Form "Correlation." Correlation. Web. 16 Jan. 2015. . Top of Form Bottom of Form "Exponential Growth and Decay. “Exponential Growth and Decay. Web. 16 Jan. 2015. . Top of Form Bottom of Form "Probability." Probability. Web. 16 Jan. 2015. . Top of Form Bottom of Form "Standard Score." Standard Score. Web. 16 Jan. 2015. . Top of Form Bottom of Form "World War Two - Causes." World War 2. Web. 16 Jan. 2015. Read More