Analysis
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). Independence
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
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). Independence
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