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Within a exponentially distributed set of data, which of the following values is always considered to...

Within a exponentially distributed set of data, which of the following values is always considered to be the most frequently occurring? A. 1 B. ? C. 0 D. None of these

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Answer #1

The mode of the exponentially distributed random variable is always 0, that is the value considered to be most frequently occuring is always 0 for an exponentially distributed data. This can be derived as follows:

The PDF for exponentially distributed variable X is given as:

Clearly the above expression would always be greater than 0. Also it would have a max value for x = 0 because for other values greater than x, the value of is always less than 1, therefore x = 0 is the required value which maximizes the above function and therefore has the highest value of occurence.

Therefore 0 is the required value here.

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