Question

the role of cauchy distribution often lies in providing counter examples .justify

Answer 1

Answer:

search it on the Google and get the answer.

Answer 2

Cauchy distribution is known as a continuous probability distribution. The caushy distribution is used in canonical example in statistics of a pathological distribution as its variance and expected value are undefined.

Explanation:

The Cauchy distribution is an example of a distribution that has no variance or no mean "higher moments" defined.  Its median and mode are are well defined and are equal to to X0. When U &  V are 2 "independent" normally" distributed random variables" with expected value zero and variance one then the ratio"U/V" has the standard"caushy distribution".

If if x is a random variable that follows a standard caushy distribution we can find that it is symmetric about 0 and median= mode =o. Its movements E(x^r) exist when  r is less than 1. Therefore the main also does not exist. Hence it is used as a counter example of a continuous distribution whose mode and mean does not exist however its symmetric and median = mode

the caushy distribution is an 'infinitely divisible probability distribution" and strictly a stable distribution