The probability distribution function of a normal variate with mean μ and variance σ^2 is given by: f(x) = 1 σ√2πe^- 1 2( x-μ σ)^2, -∞ < x < ∞, -∞ <…
CUET UG 2025 — Mathematics Algebra
The probability distribution function of a normal variate with mean μ and variance σ2 is given by:
f(x)=σ2π1e−21(σx−μ)2, −∞<x<∞, −∞<μ<∞, σ>0
If y=f(x) be the normal probability curve, then which of the following is correct?
(A) The normal curve is symmetrical about the line x=μ.
(B) Mean, median and mode of the distribution coincide.
(C) Y- axis is an asymptote to the normal curve.
(D) If x increases numerically, f(x) decreases rapidly.
Choose the correct answer from the options given below:
Held on 21 May 2025 · Verified 13 Jul 2026.
Options
- A
(A) and (D) only
- B
(A), (B) and (D) only
- C
(A), (B), (C) and (D)
- D
(B) and (C) only
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