GATE Chemical 2024 | Question: 2

Question

Consider the normal probability distribution function
\[
f(x)=\frac{4}{\sqrt{2 \pi}} e^{-8(x+3)^{2}}
\]

If $\mu$ and $\sigma$ are the mean and standard deviation of $f(x)$ respectively, then the ordered pair $(\mu, \sigma)$ is

• A. $\left(3, \frac{1}{4}\right)$
• B. $\left(-3, \frac{1}{4}\right)$
• C. $(3,4)$
• D. $(-3,4)$

Answer 1

Probability density function:

f(x) = (1/σ√2∏)e^-((x-µ)^2/(2σ^2)