What is 1/(θsqrt(2pi))e^{-((x-mu)^2)/(2(θ)^2)} ?

The solution to 1/(θsqrt(2pi))e^{-((x-mu)^2)/(2(θ)^2)} is 1/(2^{1/2)pi^{1/2}e^{((x-mu)^2)/(2θ^2)}θ}

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simplify 1/(θsqrt(2pi))e^{-((x-mu)^2)/(2(θ)^2)}

simplify

\frac{1}{θ 2 π} e^{- \frac{( x - m u ) ^{2}}{2 ( θ ) ^{2}}}

\frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}} e ^{\frac{( x - m u ) ^{2}}{2 θ ^{2}}} θ}

Solution steps

\frac{1}{θ 2 π} e^{- \frac{( x - m u ) ^{2}}{2 ( θ ) ^{2}}}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{\frac{( x - m u ) ^{2}}{2 θ ^{2}}}} \cdot \frac{1}{2 π θ}

\frac{1}{θ 2 π} = \frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}} θ}

= \frac{1}{e ^{\frac{( x - m u ) ^{2}}{2 θ ^{2}}}} \cdot \frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}} θ}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{θ \cdot 2 ^{\frac{1}{2}} π ^{\frac{1}{2}} e ^{\frac{( x - m u ) ^{2}}{2 θ ^{2}}}}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}} e ^{\frac{( x - m u ) ^{2}}{2 θ ^{2}}} θ}

e^{- y} \cdot e^{- x}

{- \frac{125}{12} : (\frac{25}{144})}^{- 1}

2^{\frac{1}{2}} (2^{\frac{1}{2}} \cdot 3^{\frac{3}{4}})

(16 n^{5}) (4 n^{3})

(2 x^{4 - \frac{1}{4 x ^{6}}})^{8}

What is 1/(θsqrt(2pi))e^{-((x-mu)^2)/(2(θ)^2)} ?
The solution to 1/(θsqrt(2pi))e^{-((x-mu)^2)/(2(θ)^2)} is 1/(2^{1/2)pi^{1/2}e^{((x-mu)^2)/(2θ^2)}θ}