Question

“YOUR” Story, Sampling Methods, Discrete Variables, and Continuous Variables.         

1) Identify and Explain ---

A personal example. This should be a unique “Story” you will use on the rest of the exam.

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2) Define the Population and take a Sample ---

Provide an example of a Finite population you could have used in your “Story” and explain how you would have used one of the sampling methods.

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Provide an example of an Infinite population you could have used in your “Story” and explain how you would have used one sampling methods

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3) Identify and briefly explain ---

A discrete binomial variable (xi) you could have used in your decision.

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A discrete multinomial variable (xi) you could have used in your decision.

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A continuous Normally distributed variable (xi) you could have used in your decision.

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A continuous Exponentially distributed variable (xi) you could have used in your decision.

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Answer 1

1) Consider a mall in city A undergoing a survey , wherein they are collecting the data of height of customers and interarrival time between the two consecutive customers buying denims. This survey is for them to make an estimate of how many number of each size of denims of a particular brand to be ordered so that the inventory is emptied within a week or shorter possible span and how many denins would sold in a day.

2) In the story above the finite population considered is the customers visiting the mall for shopping denims in a week (suppose 2k). Now we take sample of approx. 100 people from population using simple random sampling without replacement and collect the required data of height.

3) i) Discrete binomial distribution - we use distribution to know the probability of 'n' number of customers will buy denims out of all customers coming to the mall.

ii) Discrete multinomial distribution - we use this to know the probability of n=(n1,n2,n3,..) customers buying each size of denims .. using which we predict the estimate of number of each sizes of denims to be ordered.

iii) Normal distribution - we have a continuous variate which is heights of customers buying denims which is approximately fitting a normal distribution. This way we can predict the highest number of denims of which size are to be ordered by mean of this normal variate.

iv) Exponential distribution - The interarrival time between the two customers buying denims is said to follow exponential distribution. This way we can predict expected number of denims which would be sold in the mall in a day.