Quantative methods report Essay Example | Topics and Well Written Essays - 3000 words

Quantative methods report - Essay Exampleof categorical variables 2. The measures of center field includes arithmetic mean, geometric mean, harmonic mean, median and mode where as the measures of spread ar addicted by range, mean deviation, quartile deviation and standard deviation. The measures of shape are skewness and measures of position is kurtosis. 3. Event Any application subjected to experiment is called as an event. For example in tossing of an unbiased coin (experiment) the occurrence of head and tail are events. Since in any unbiased coin both head or tail butt joint occur, they aim together in a set is known as specimen space. The archetype space in a coin tossing experiment is S=H,T. Similarly the sample space in throwing of a blow over is S=1,2,3,4,5,6. Marginal probability is a measure of occurrence of an event keeping the occurrence of the early(a) event as constant in jointly occurring events. The probability of joint occurrence of two events either indepe ndent or dependent is p(x,y)=pij where i=1 to m j=1 to n when x and y are discrete or else f(x,y)=fxy where x and y are both unceasing. 4. The sideboard is an anticipate value for an investment involving normal percentage values whereas the risk is the measure of uncertainity usually having a banish impact on return. The risk as per standard norms is 1 and if the value of risk is below 1 it is considered to be less risky and if the value of risk is above 1, it is considered to be highly risky. Suppose the return and risk involved in an investment is given in the following table as shelve 2 Sample table indicating nature of investment Investment nature Stocks Bonds Real Estate chance for investing 0.4 0.25 0.35 Return % 13% 8% 10% Risk 1.2 0.85 1.25 Note The total investment is 250,000 (say), we can formulate a strategy to maximize the return based on the risk and return involved. separate distribution is concerned with the distribution of a variable which is countable or fini te. For example in tossing of a die, the outcome is a discrete hit-or-miss variable and its distribution of the outcomes 1,2,3,4,5 and 6 can be expound in the form P(X=x)=pi= where x takes any value 1,2,3,4,5 or 6 whereas a continuous random variable takes any value between a range of values (in an interval) for example if the frequence of arrival of a stack is 30 minutes and if we define the waiting time for a bus as a continuous random variable x, then the distribution of waiting time is given by f(x)= 0?x?30 =0 otherwise. 5. The sampling distribution is a distribution of the sample measures where the sample of size n is drawn out of a creation of size N. If any random sample of size n is taken from a normal population of size N, then the sample mean is x and the distribution of sample mean is having expected value ? and variance ?2/n. ie. if the population is normal with mean ? and variance ?, then the sample will be having mean with E()=? and SD is SE()= . The central res triction theorem says that if a sample of size n having values x1, x2, x3.......,xn follows normal distribution with mean ? and v