I need a discussion response to my peers post To what shape does the histogram c

Question

I need a discussion response to my peers post

To what shape does the histogram converge when you roll 1 die at a time? What happens when you roll a pair of dice? When you roll 3 dice? 4 dice? 5 dice?

Set to 1-the convergence is a uniform shape with solid red columns that goes from 1 to 6

Set to 2: the convergence is a symmetry graph that goes from 2 to 12

Set to 3: the convergence is a graph that goes from 3 to 18

Set to 4: the convergence is a graph that goes from 4 to 24

Set to 5: the convergence is a graph that goes from 5 to 30

As you increase the number of dice the bell shape gets more and more define, always increasing at the end by six.

Discuss a normal distribution and what it implies. Are there other distribution patterns?

A normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme. A graphical representation of a normal distribution is called a bell curve, this may vary according to the distribution of the population but the peak is always in the middle and the curve is always symmetrical. The normal distribution is defined by two parameters, the mean and the standard deviation.

Another distribution is called the Poisson distribution which is applied when the event is something that can be counted in whole numbers. Occurrences are independent, so that one occurrence neither diminishes nor increases the chance of another. The Poisson distribution is most often used for rare events, and it is only with rare event that it can be successfully mimic the Binomial Distribution.

Reference: Statistics How To retrieve on November 28, 2017 from http://www.statisticshowto.com/probability-and-statistics/non-normal-distributions/

Explanation / Answer

Assuming what you have posted is your peers post and you want response to it.

Yes , on increasng the number of dice the curve will get more defined as the number of points is increasing which can be written 5n+1. as n tends to be large the number of points will be high and curve will be more smooth. Few other observations are:

1. Curve will be getting shifted towards right , with peak at 3n+1.

2. End is shifting by 6 as mentioned, similiarly the peak will get shifted by 3 with each increasing number of n. This ensures the symmetry of the curve.

Distribution in the nature follows diferent pattern which justifies different distributions. These can be classified in two major categories normal and non-normal distribution.

Normal distribution: Most patterns follows this distribtution, it has central tendency with symmetry on both side. The shape of the curve is defined by two parameters mean and variance. Less the variance is more steep is the curve. normal distribution are used by corpaorates to bring efficiency in the production using six-sigma model.

The position of the curve is given by the mean.

Non Normal distribution:

many datas doesn't fit on normal. e.g growth of bacteria follows exponential law, number of accidents tends to follow the poisson distribution.

Exponential distribution: It is derived form of the waiting interval between successive changes in the poisson distribution.

There are many things to discuss, if you can let me know in which direction you want to take the discussion it will be more helpful.

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