A random variable, X, is defined as X ~ Geo(p). I know the mode is...

glitinosim3

glitinosim3

Answered

2022-07-09

A random variable, X, is defined as X ~ Geo(p). I know the mode is 1 as it is the value of X with highest probability.
How do i show this? As this is a discrete R.V, can i be allowed to use Calculus?

Answer & Explanation

Jayvion Tyler

Jayvion Tyler

Expert

2022-07-10Added 23 answers

The probability distribution, as you've set it out, is
P ( X = k ) = ( 1 p ) k 1 p k N
It should then be simple to show that for any integer k > 1,
P ( X = 1 ) = p > ( 1 p ) k 1 p = P ( X = k )
provided 0 < p < 1, so that 0 < 1 p < 1 and 0 < ( 1 p ) k 1 < 1.

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