Question
Download Solution PDFFor 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
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
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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