Question

In: Statistics and Probability

Suppose the following 25 values were sampled from a uniform distribution between 0 and 1. 0.095...

Suppose the following 25 values were sampled from a uniform distribution between 0 and 1.

0.095	0.242	0.966	0.738	0.756
0.302	0.138	0.873	0.554	0.516
0.135	0.714	0.301	0.661	0.443
0.335	0.812	0.981	0.882	0.138
0.669	0.379	0.112	0.501	0.535

Convert the above 25 values to one that is sampled from an exponential distribution with parameter 5:

The number of “converted values” that are less than 0.0446 is 1.
The number of “converted values” that are in the range [0.0446, 0.1022) is 2.
The number of “converted values” that are in the range [0.1022, 0.1833) is 3.
The number of “converted values” that are in the range [0.1833, 0.3219) is 4.
The number of “converted values” that are at least 0.3219 is 5.

Expert Solution

Hey I have used excel for calculation

Its an interesting question. I have used commonly used inverse transform method. in theory the formula is derived like this...

Now using this formula in excel I got this..

frequency i.e number of variates for corresponding ranges are counted using countif or countifs .

Interestingly in each range I got equal values not like what you have mentioned in the question.To double check I color coded values for corresponding ranges and you can count the colored cell for specific range and it matches with our count.

so in each range we have 5 values total becomes 25.

These are formulas in excel that i have used.

This is because of your specific data.

When I generate some random uniform values and did the same process I got

6 values between 0.1022 to 0.1833 so the result of 5 values in each is specific to your data.

Please upvote if was able to help you

Thanks

orchestra answered 2 years ago

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