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For the discrete random variable X having probability mass function (1 - p)k - 1p; k = 1, 2, 3,...; 0 < p ≤ 1, the mode of X is

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SSC CGL Tier-II ( JSO ) 2019 Official Paper ( Held On : 17 Nov 2020 )
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  1. 1
  2. 0
  3. p 
  4. 1 - p

Answer (Detailed Solution Below)

Option 1 : 1
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Detailed Solution

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Given

PMF = (1 - p)k - 1p

Concept used 

Mode is the value of x for which f(x) is the maximum. IIt can be obtained by equating the first derivative of f(x) to zero and checking that the second derivative of f(x)  is negative I;e

F’(x) = 0 and f’’(x) < o

Calculation

This PMF is in geometric expression and the mode of geometric distribution is 1

∴ Mode of X is 1

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