Differences between discrete and continuous random variables (probability distri

Question

Differences between discrete and continuous random variables (probability distributions) Provide business examples of discrete and continuous variables Uniform distribution Properties and assumptions Business applications Related calculations Probability Expected value and standard deviation Interpretations of results (see class examples) Exponential distribution Properties and assumptions Business applications Related calculations Probability Interpretations of results (see class examples) Normal distribution Properties and assumptions (see powerpoint slides) Business applications Z transformation and Z score Calculations of probability with the use of Z table Calculations of cutoff value (given percentile) with the use of Z table Interpretations of results (see class examples) Sampling and Sampling Distribution Concepts What arc population parameters? Finite vs. infinite population What is sampling? Why do we need to conduct sampling? What are the t

Explanation / Answer

These are very general and basic topics in statistics and sufficient amount of theory can be found in any university level statistics text books. However I have included here a brief introduction of each topic.

f(x) = 1/2exp(-(x-µ)2/22) for all real values of X. 2 > 0 and µ takes only real values. For a normal distribution the mean median and mode are the same i.e the distribution is symmetric. An example could be the demand a commodity on a particular day say the number of Kellogs packets sold at a departmental store on a day will follow a normal distribution.

The Z transforms can be obtained as Z= X-µ/ and the process is Z-transformations. This is called a standard normal variate and it follows a standard normal distribution. This is also called the Z-score of the value X. Z tables are available which gives the probability of the standard random variable taking a value less than that particular value i.e P(Z<z). These are widely used to calculate normal probabilities. Cutoffs values are basically those values for which we reject all observations which take a value less than or greater than that particular value dpending on the situation.

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