Question

For the discrete random variable X having probability mass function (1 - p)^{k - 1}p; k = 1, 2, 3,...; 0 < p ≤ 1, the mode of X is
1. 1
2. 0
3. p 
4. 1 - p

Answer 1

Correct Answer - Option 1 : 1

Given

PMF = (1 - p)^{k - 1}p

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