Amol,you should have learned some basic statistical ...



Amol,you should have learned some basic statistical concepts that can be very useful in reasoning many business applications. In stepwise fashion, these are:

1.To solve a business problem, you must have data illustrating the problem (examples: variable cost, and fixed cost data, demand/price data, supply/price data, employee safety records, people income, etc).

2. You can use descriptive statistics and frequency distribution to describe the data and reveal any abnormality.

3. You can develop relationships between variables

4. You can create a sampling distribution to estimate population parameters from sample statistics

5. You can determine probabilities and create a probability distribution

Based on your readings, Explain the difference between theoretical probability and actual probability.

Actual probability - When we determine the probability of an event

empirically, we perform a large number of trials of an experiment and

compute the ratio

Number of time the even occurs / number of trials.

This ratio gives us a good estimate of how likely it is for the event

to occur in future trials of the experiment. This is the actual probability which is dependent on actually experiment

Theoretical Probability - The theoretical probability of the event is the fraction:

# ways the event can occur

total possible outcomes

It is based on the expected outcome for an event.

Lets do an expirement of fliiping 230 coins and we need the probability of number of heads.

The theoretical probability of the event is the fraction:

# ways the event can occur

total possible outcomes

Referring to the situation above, the theoretical probability of the event that heads comes up is:

P(H) = 1/2 = 0.5 = 50%

The experimental/actual probability for equally likely events is the fraction:

# favourable outcomes

total outcomes

Referring to the situation above, the experimental probability of the event that heads comes up is:

P(H) = 13/20 = 0.65 = 65%

Also, explain the difference between a sampling distribution and a probability distribution.

A probability distribution is a table or an equation that links each outcome of a statistical experiment with its probability of occurence. Consider the coin flip experiment in which we flip two coins. The table below, which associates each outcome with its probability, is an example of a probability distribution.

|Number of heads |Probability |

|0 |.25 |

|1 |.50 |

|2 |.25 |

The above table represents the probability distribution of the random variable X.

Sampling distribution is the probability distribution, under repeated sampling of the population, of a given statistic (a numerical quantity calculated from the data values in a sample). Suppose further that we compute a statistic (e.g., a mean, proportion, standard deviation) for each sample. The probability distribution of this statistic is called a sampling distribution.

Use examples to illustrate the difference. Discussing this question will prove to you that “Probability Distribution” is perhaps the most powerful analytical tool that you will ever learn and use in numerous applications. A key advice in this regard "Think Random Number Generator"

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