簡約 1/(sqrt(2pi))e^{-(0.5^2)/2}

解

簡約

\frac{1}{2 π} e^{- \frac{0. 5 ^{2}}{2}}

0.35206 \dots

解答ステップ

\frac{1}{2 π} e^{- \frac{0. 5 ^{2}}{2}}

指数の規則を適用する:

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

= \frac{1}{2 π} \cdot \frac{1}{e ^{\frac{0. 5 ^{2}}{2}}}

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

= \frac{1}{e ^{\frac{0. 5 ^{2}}{2}}} \cdot \frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}}

分数を乗じる:

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

= \frac{1 \cdot 1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}} e ^{\frac{0. 5 ^{2}}{2}}}

数を乗じる:

1 \cdot 1 = 1

= \frac{1}{2 ^{\frac{1}{2}} e ^{\frac{0. 5 ^{2}}{2}} π ^{\frac{1}{2}}}

0. 5^{2} = 0.25

= \frac{1}{2 ^{\frac{1}{2}} e ^{\frac{0.25}{2}} π ^{\frac{1}{2}}}

元を10進法形式に変換する

2^{\frac{1}{2}} = 1.41421 \dots

= \frac{1}{1.41421 \dots e ^{\frac{0.25}{2}} π ^{\frac{1}{2}}}

元を10進法形式に変換する

π^{\frac{1}{2}} = 1.77245 \dots

= \frac{1}{1.41421 \dots \cdot 1.77245 \dots e ^{\frac{0.25}{2}}}

e^{\frac{0.25}{2}} = 1.13314 \dots

= \frac{1}{1.41421 \dots \cdot 1.77245 \dots \cdot 1.13314 \dots}

数を乗じる:

1.41421 \dots \cdot 1.77245 \dots \cdot 1.13314 \dots = 2.84038 \dots

= \frac{1}{2.84038 \dots}

数を割る:

\frac{1}{2.84038 \dots} = 0.35206 \dots

= 0.35206 \dots