# Write down the probability function of a normal variate

29 views
Write down the probability function of a Normal variate which has mean 8 and variance 9

+1 vote
by (45.7k points)

Given, mean  μ = 8 and

variance σ2 = 9 ⇒ σ = $\sqrt9$ = 3

Probability function is normal distribution whose variance σ2 and mean μ is

P(x,σ,μ) = $\frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{1}{2}\big(\frac{\mathrm{x}-\mu}{\sigma}\big)^2}$ , x ∈ R

then probability function for given problem is

P(x,σ,μ) = $\frac{1}{3\sqrt{2\pi}}e^{-\frac{1}{2}\big(\frac{\mathrm{x}-8}{3}\big)^2}$

$\frac{1}{3\sqrt{2\pi}}e^{-\frac{1}{18}(\mathrm{x}-8)^2}$ , x ∈ R