A probability distribution is a function that provides the probability of occurrence of different potential outcomes of an experiment. It is a description of an event regarding possibilities of events, e.g., the results of a survey. It is usually based on a set of sample space which includes all potential outcomes of an observed random phenomenon. There are two types; discrete which is applicable in distinct situations like tossing a coin and a continuous distribution which is appropriate for scenarios where potential outcomes take in values in a continuous range (Beri, 2010; Sharpe & Velleman, 2011).
A random variable is one whose potential values are numerical outputs of a random observation. A random variable has to be measured, and its domain is a set of possible outcomes. In tossing a coin, for example, there are only two outcomes, i.e., a tail or head and since either of these outcomes occurs, it should not have a zero probability. Random variables map possible outcomes to numerical quantities. They can represent future or past experiments. Random variables contain probability distributions that specify the possibility that the possible values lie in a given interval (Beri, 2010; Sharpe & Velleman, 2011).
Delegate your assignment to our experts and they will do the rest.
In an example of tossing a coin three time, the sample space can be. The random variable X that represents the number of tails when the coin is tossed three times takes the value 0,1,2 and 3, and the probability distribution for the test can be given as follows;
| Number of trials X | Probability | Expected value | X^2p(x) |
| 0 | 1/8 | 0 | 0 |
| 1 | 3/8 | ¼ | ¼ |
| 2 | 3/8 | ½ | 1 |
| 3 | 1/8 | 3/8 | 9/8 |
| Sum | 1 | 9/8 | 19/8 |
Variance =18/8 –(9/8)^2 =71/64 =1.109375
Standard deviation = square root of variance =1.0532687216
The probability of having a X number of heads when a coin is tossed six times can be computed using the following model. In this case, the expected distribution of a random sample X if the n factorials and the likelihood of each occurrence are known.
P(X) = n!/X!(n-X)! Π X (1- π)^n-X
When a coin is tossed six times, the likelihood of X heads can be computed using n = six trials, π =0.5, X number of heads in the six tosses. X is the binomial distribution with π =0.5 and n = 6.
X ~ B 96,0.5). The computed probability distribution is symmetrical since the probability of heads is equal to that of tails =0.5. The binomial distribution for X in six coin tosses can be shown as follows (John, Whitaker, Johnson & John, 2006)
| X | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| Probability | 0.0156 | 0.094 | 0.234 | 0.3125 | 0.234 | 0.094 | 0.0156 |
Business decisions are related to different aspects of probability. In calculating various statistics, the underlying concepts determine whether and by how much the interaction of events affect probability. Probability concepts and statistical calculations are critical to making sound business decisions, especially where uncertainty is involved. Concepts in probability are abstracts that managers use to identify the degree of risk any business decision will require. In the determination of probability, the risk is the level at which an outcome differs from the expected benchmark. Probability knowledge can be helpful in the decision-making process of any business especially in identifying, weighing and selecting alternatives. Probability is still useful at earlier stages of decision identification and gathering relevant information (Sweeney, Williams & Anderson, 201).
A normal distribution is a continuous probability distribution that is used in statistics and natural and social sciences to demonstrate real value variables with unknown distribution. They are essential because of the central limit theorem. The average of observed sample elements drawn from independent distributions is typically distributed if a significant number of observations made. Managers use normal distributions for decision making concerning the allocation of variables and to identify outliers that might affect the overall results (Groebner, 2011; Sweeney, Williams & Anderson, 2011).
Binomial probability is a distribution with n and p parameters that shows the number of successes in n experiments with each accepting or rejecting and having its Boolean valued outcome. One test is known as Bernoulli trial while a sequence is known as Bernoulli Process. For one experiment, the distribution is known as Bernoulli distribution which forms the basis for binomial tests. The distribution is usually used to determine the number of success in a sample drawn with replacement (Groebner, 2011).
Microsoft Excel can be used to create charts, graphs, and other descriptive statistics. To create charts and graphs, use the insert functions and select charts and graphs depending on your choice. To compute descriptive statistics, select data analysis at the data tab then highlight descriptive statistics and select the data to be described then press ok.
References
Beri, G. C. (2010). Business statistics . New Delhi: Tata McGraw-Hill.
Groebner, D. E. (2011.). Business statistics: a decision-making approach . 8th ed.: Pearson
John, J. A., Whitaker, D., Johnson, D. G., & John, J. A. (2006). Statistical thinking in business . Boca Raton: Chapman & Hall/CRC.
Sharpe, N. R., D., D. V., & Velleman, P. F. (2011). Business statistics: a first course . Boston: Pearson.
Sweeney, D. J., A., Williams, T. A., & Anderson, D. R. (2011). Fundamentals of business statistics . Mason, OH: South-Western.
