The probability density function of a normal random variable X, with mean μ and standard deviation σ, is given by:

CA Foundation · Quantitative Aptitude · MTP · September 2026
The probability density function of a normal random variable X, with mean μ and standard deviation σ, is given by:
(A) A. f(x) = 1 / σ√(2Π) .e - (x-μ) 2 / 2σ 2 , for 0 < x < ∞
(B) B. f(x) = 1 / √(2Π)σ .e - (x-μ) 2 / 2σ 2 , for - ∞ < x < ∞
(C) C. f(x) = 1 / σ√(2Π) .e - (x-μ) 2 / 2σ 2 , for - ∞ < x < ∞
(D) D. None of these

Suggested Answer and Working Notes:

Correct Answer: Option (C)

C. f(x) = 1 / σ√(2Π) .e - (x-μ) 2 / 2σ 2 , for - ∞ < x < ∞

Topics: Part-C: Statistics

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