Assignment Week 1
Answer the following questions:
1. Describe the rationale for utilizing probability concepts. For practical reasons, variables are observed to collect data. The sampled data is then analyzed to elicit information for decision making in business and indeed in all human endeavors. However, sampled information is incomplete and not free from sampling error. Its use in decision-making processes introduces an element of chance. Therefore, it is important for a decision-maker to know the amount of chance associated with a statistical decision of it being wrong. To quantify the amount of chance due to sampling error, basic probability concepts are indispensable via modeling sampled populations and testing of research hypotheses. Probability is the guide for a "good" life and successful business. The concept of probability occupies an important place in the decision-making process. Few decision making situations is perfect information - all the needed facts - available. Most decisions are made in the face of uncertainty. Probability enters into the process by playing the role of a substitute for certainty - a substitute for complete knowledge.
Is there more than one type of probability? If so, describe the different types of probability. The probability of an event A given the information that an event B has occurred is denoted by P(A/B). It is called the conditional probability.
P(AandB) = P(A/B) P(B) or P(A and B) = P(B/A)P(A).
Two events A and B are statistically independent if the following equivalent statements hold. i) P(A) = P(A/B), ii) P(B) = P(B/A), iii) P(A and B) = P(A) P(B) To prove independence of two events, check any one of the three equivalent statements. 2. Briefly discuss probability distributions.
A probability distribution gathers together all possible outcomes of a random variable (i.e. any quantity for which more than one value is possible), and summarizes these outcomes by indicating the probability of each of them. While a probability distribution is often associated with the bell-shaped curve, recognize that such a curve is only indicative of one specific type of probability, the so-called normal probability distribution. The CFA curriculum does focus on normal distributions since they frequently apply to financial and investment variables, and are used in hypothesis testing. However, in real life, a probability distribution can take any shape, size and form. This is where the above answer came from (Read more: http://www.investopedia.com/exam-guide/cfa-level-1/quantitative-methods/probability-distributions.asp#ixzz1hBEEC8QK) When you want to describe probability for a continuous variable, you do so by describing a certain area. A large area implies a large probability and a small area implies a small probability. Some people don't like this, because it forces them to remember a bit of geometry (or in more complex situations, calculus). But the relationship between probability and area is also useful, because it provides a visual interpretation for probability.
What is a normal distribution?
Normal Distribution is a statistical model which is often used to show why sampling is necessary. It tells a business what the expected range of outcomes from a particular population/product will be and useful where businesses use a large scale sample. Normal Distribution is a symmetrical frequency distribution, which can be split in 2 equal halves, so that the mean, mode and median are equal. It is the spread of the data that determins the steepness or shallowness of the curve. The spread is measured by the Standard Deviation which measures how far on average a figure is from the mean of a distribution. The normal distribution is pattern for the distribution of a set of data which follows a bell shaped curve. The bell shaped curve has several properties:
The curve concentrated in the center and decreases on either side. This means that the data has...
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