Find the mean, variance, and standard deviation of the probability distribution. X P(x) 2 0.1 5 4 0.2 0 6 0.2 5 8 0.3
Find the mean, variance, and standard deviation of the probability distribution.X P(x)2 0.154 0.206 0.258 0.35
10 0.05
Find the mean, variance, and standard deviation of the probability distribution.X P(x)2 0.154 0.206 0.258 0.35
10 0.05
๐=โ [๐ฅ โ๐ (๐ฅ )]
Find the mean, variance, and standard deviation of the probability distribution.X P(x)2 0.154 0.206 0.258 0.35
10 0.05
๐=โ [๐ฅ โ๐ (๐ฅ )]Create a column of xโP(x)
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x)2 0.154 0.206 0.258 0.3510 0.05
๐=โ [๐ฅ โ๐ (๐ฅ )]Create a column of xโP(x)
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x)2 0.15 2(0.15) = 0.304 0.206 0.258 0.3510 0.05
๐=โ [๐ฅ โ๐ (๐ฅ )]Create a column of xโP(x)
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x)2 0.15 2(0.15) = 0.304 0.20 4(0.20) = 0.806 0.258 0.3510 0.05
๐=โ [๐ฅ โ๐ (๐ฅ )]Create a column of xโP(x)
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x)2 0.15 2(0.15) = 0.304 0.20 4(0.20) = 0.806 0.25 6(0.25) = 1.508 0.3510 0.05
๐=โ [๐ฅ โ๐ (๐ฅ )]Create a column of xโP(x)
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x)2 0.15 2(0.15) = 0.304 0.20 4(0.20) = 0.806 0.25 6(0.25) = 1.508 0.35 8(0.35) = 2.8010 0.05
๐=โ [๐ฅ โ๐ (๐ฅ )]Create a column of xโP(x)
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x)2 0.15 2(0.15) = 0.304 0.20 4(0.20) = 0.806 0.25 6(0.25) = 1.508 0.35 8(0.35) = 2.8010 0.05 10(0.05) = 0.50
๐=โ [๐ฅ โ๐ (๐ฅ )]Create a column of xโP(x)
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x)2 0.15 2(0.15) = 0.304 0.20 4(0.20) = 0.806 0.25 6(0.25) = 1.508 0.35 8(0.35) = 2.8010 0.05 10(0.05) = 0.50
๐=โ [๐ฅ โ๐ (๐ฅ )]
Sum the column of xโP(x)
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x)2 0.15 2(0.15) = 0.304 0.20 4(0.20) = 0.806 0.25 6(0.25) = 1.508 0.35 8(0.35) = 2.8010 0.05 10(0.05) = 0.50
๐=โ [๐ฅ โ๐ (๐ฅ )]
Sum the column of xโP(x)
ฮฃ[xโP(x)]=5.9
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x)2 0.15 2(0.15) = 0.304 0.20 4(0.20) = 0.806 0.25 6(0.25) = 1.508 0.35 8(0.35) = 2.8010 0.05 10(0.05) = 0.50
๐=โ [๐ฅ โ๐ (๐ฅ )]=5.9
ฮฃ[xโP(x)]=5.9
Mean
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x)2 0.15 2(0.15) = 0.304 0.20 4(0.20) = 0.806 0.25 6(0.25) = 1.508 0.35 8(0.35) = 2.8010 0.05 10(0.05) = 0.50
๐=โ [๐ฅ โ๐ (๐ฅ )]=5.9
ฮฃ[xโP(x)]=5.9
๐ 2=โ [๐ฅ2 โ๐ (๐ฅ )]โ๐2
Create a column of x2
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x) x22 0.15 2(0.15) = 0.304 0.20 4(0.20) = 0.806 0.25 6(0.25) = 1.508 0.35 8(0.35) = 2.80
10 0.05 10(0.05) = 0.50
๐=โ [๐ฅ โ๐ (๐ฅ )]=5.9
ฮฃ[xโP(x)]=5.9
๐ 2=โ [๐ฅ2 โ๐ (๐ฅ )]โ๐2
Create a column of x2
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x) x22 0.15 2(0.15) = 0.30 22 = 44 0.20 4(0.20) = 0.806 0.25 6(0.25) = 1.508 0.35 8(0.35) = 2.80
10 0.05 10(0.05) = 0.50
๐=โ [๐ฅ โ๐ (๐ฅ )]=5.9
ฮฃ[xโP(x)]=5.9
๐ 2=โ [๐ฅ2 โ๐ (๐ฅ )]โ๐2
Create a column of x2
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x) x22 0.15 2(0.15) = 0.30 22 = 44 0.20 4(0.20) = 0.80 42 = 166 0.25 6(0.25) = 1.508 0.35 8(0.35) = 2.80
10 0.05 10(0.05) = 0.50
๐=โ [๐ฅ โ๐ (๐ฅ )]=5.9
ฮฃ[xโP(x)]=5.9
๐ 2=โ [๐ฅ2 โ๐ (๐ฅ )]โ๐2
Create a column of x2
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x) x22 0.15 2(0.15) = 0.30 22 = 44 0.20 4(0.20) = 0.80 42 = 166 0.25 6(0.25) = 1.50 62 = 368 0.35 8(0.35) = 2.80
10 0.05 10(0.05) = 0.50
๐=โ [๐ฅ โ๐ (๐ฅ )]=5.9
ฮฃ[xโP(x)]=5.9
๐ 2=โ [๐ฅ2 โ๐ (๐ฅ )]โ๐2
Create a column of x2
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x) x22 0.15 2(0.15) = 0.30 22 = 44 0.20 4(0.20) = 0.80 42 = 166 0.25 6(0.25) = 1.50 62 = 368 0.35 8(0.35) = 2.80 82 = 6410 0.05 10(0.05) = 0.50
๐=โ [๐ฅ โ๐ (๐ฅ )]=5.9
ฮฃ[xโP(x)]=5.9
๐ 2=โ [๐ฅ2 โ๐ (๐ฅ )]โ๐2
Create a column of x2
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x) x22 0.15 2(0.15) = 0.30 22 = 44 0.20 4(0.20) = 0.80 42 = 166 0.25 6(0.25) = 1.50 62 = 368 0.35 8(0.35) = 2.80 82 = 6410 0.05 10(0.05) = 0.50 102 = 100
๐=โ [๐ฅ โ๐ (๐ฅ )]=5.9
ฮฃ[xโP(x)]=5.9
๐ 2=โ [๐ฅ2 โ๐ (๐ฅ )]โ๐2
Create a column of x2
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x) x22 0.15 2(0.15) = 0.30 22 = 44 0.20 4(0.20) = 0.80 42 = 166 0.25 6(0.25) = 1.50 62 = 368 0.35 8(0.35) = 2.80 82 = 64
10 0.05 10(0.05) = 0.50 102 = 100
๐=โ [๐ฅ โ๐ (๐ฅ )]=5.9
ฮฃ[xโP(x)]=5.9
๐ 2=โ [๐ฅ2 โ๐ (๐ฅ )]โ๐2
Create a column of x2โP(x)
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x) x2 x2โP(x)2 0.15 2(0.15) = 0.30 22 = 4
4 0.20 4(0.20) = 0.80 42 = 16
6 0.25 6(0.25) = 1.50 62 = 36
8 0.35 8(0.35) = 2.80 82 = 64
10 0.05 10(0.05) = 0.50 102 = 100
๐=โ [๐ฅ โ๐ (๐ฅ )]=5.9
ฮฃ[xโP(x)]=5.9
๐ 2=โ [๐ฅ2 โ๐ (๐ฅ )]โ๐2
Create a column of x2โP(x)
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x) x2 x2โP(x)2 0.15 2(0.15) = 0.30 22 = 4 4(0.15) = 0.604 0.20 4(0.20) = 0.80 42 = 16
6 0.25 6(0.25) = 1.50 62 = 36
8 0.35 8(0.35) = 2.80 82 = 64
10 0.05 10(0.05) = 0.50 102 = 100
๐=โ [๐ฅ โ๐ (๐ฅ )]=5.9
ฮฃ[xโP(x)]=5.9
๐ 2=โ [๐ฅ2 โ๐ (๐ฅ )]โ๐2
Create a column of x2โP(x)
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x) x2 x2โP(x)2 0.15 2(0.15) = 0.30 22 = 4 4(0.15) = 0.604 0.20 4(0.20) = 0.80 42 = 16 16(0.20) = 3.206 0.25 6(0.25) = 1.50 62 = 368 0.35 8(0.35) = 2.80 82 = 64
10 0.05 10(0.05) = 0.50 102 = 100
๐=โ [๐ฅ โ๐ (๐ฅ )]=5.9
ฮฃ[xโP(x)]=5.9
๐ 2=โ [๐ฅ2 โ๐ (๐ฅ )]โ๐2
Create a column of x2โP(x)
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x) x2 x2โP(x)2 0.15 2(0.15) = 0.30 22 = 4 4(0.15) = 0.604 0.20 4(0.20) = 0.80 42 = 16 16(0.20) = 3.206 0.25 6(0.25) = 1.50 62 = 36 36(0.25) = 9.008 0.35 8(0.35) = 2.80 82 = 64
10 0.05 10(0.05) = 0.50 102 = 100
๐=โ [๐ฅ โ๐ (๐ฅ )]=5.9
ฮฃ[xโP(x)]=5.9
๐ 2=โ [๐ฅ2 โ๐ (๐ฅ )]โ๐2
Create a column of x2โP(x)
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x) x2 x2โP(x)2 0.15 2(0.15) = 0.30 22 = 4 4(0.15) = 0.604 0.20 4(0.20) = 0.80 42 = 16 16(0.20) = 3.206 0.25 6(0.25) = 1.50 62 = 36 36(0.25) = 9.008 0.35 8(0.35) = 2.80 82 = 64 64(0.35) = 22.40
10 0.05 10(0.05) = 0.50 102 = 100
๐=โ [๐ฅ โ๐ (๐ฅ )]=5.9
ฮฃ[xโP(x)]=5.9
๐ 2=โ [๐ฅ2 โ๐ (๐ฅ )]โ๐2
Create a column of x2โP(x)
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x) x2 x2โP(x)2 0.15 2(0.15) = 0.30 22 = 4 4(0.15) = 0.604 0.20 4(0.20) = 0.80 42 = 16 16(0.20) = 3.206 0.25 6(0.25) = 1.50 62 = 36 36(0.25) = 9.008 0.35 8(0.35) = 2.80 82 = 64 64(0.35) = 22.40
10 0.05 10(0.05) = 0.50 102 = 100 100(0.05) = 5.00
๐=โ [๐ฅ โ๐ (๐ฅ )]=5.9
ฮฃ[xโP(x)]=5.9
๐ 2=โ [๐ฅ2 โ๐ (๐ฅ )]โ๐2
Create a column of x2โP(x)
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x) x2 x2โP(x)2 0.15 2(0.15) = 0.30 22 = 4 4(0.15) = 0.604 0.20 4(0.20) = 0.80 42 = 16 16(0.20) = 3.206 0.25 6(0.25) = 1.50 62 = 36 36(0.25) = 9.008 0.35 8(0.35) = 2.80 82 = 64 64(0.35) = 22.40
10 0.05 10(0.05) = 0.50 102 = 100 100(0.05) = 5.00
๐=โ [๐ฅ โ๐ (๐ฅ )]=5.9
ฮฃ[xโP(x)]=5.9
๐ 2=โ [๐ฅ2 โ๐ (๐ฅ )]โ๐2
Sum the column of x2โP(x)
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x) x2 x2โP(x)2 0.15 2(0.15) = 0.30 22 = 4 4(0.15) = 0.604 0.20 4(0.20) = 0.80 42 = 16 16(0.20) = 3.206 0.25 6(0.25) = 1.50 62 = 36 36(0.25) = 9.008 0.35 8(0.35) = 2.80 82 = 64 64(0.35) = 22.40
10 0.05 10(0.05) = 0.50 102 = 100 100(0.05) = 5.00
๐=โ [๐ฅ โ๐ (๐ฅ )]=5.9
ฮฃ[xโP(x)]=5.9
๐ 2=โ [๐ฅ2 โ๐ (๐ฅ )]โ๐2
Sum the column of x2โP(x)ฮฃ[x2โP(x)]=40.2
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x) x2 x2โP(x)2 0.15 2(0.15) = 0.30 22 = 4 4(0.15) = 0.604 0.20 4(0.20) = 0.80 42 = 16 16(0.20) = 3.206 0.25 6(0.25) = 1.50 62 = 36 36(0.25) = 9.008 0.35 8(0.35) = 2.80 82 = 64 64(0.35) = 22.40
10 0.05 10(0.05) = 0.50 102 = 100 100(0.05) = 5.00
๐=โ [๐ฅ โ๐ (๐ฅ )]=5.9
ฮฃ[xโP(x)]=5.9 ฮฃ[x2โP(x)]=40.2Variance
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x) x2 x2โP(x)2 0.15 2(0.15) = 0.30 22 = 4 4(0.15) = 0.604 0.20 4(0.20) = 0.80 42 = 16 16(0.20) = 3.206 0.25 6(0.25) = 1.50 62 = 36 36(0.25) = 9.008 0.35 8(0.35) = 2.80 82 = 64 64(0.35) = 22.40
10 0.05 10(0.05) = 0.50 102 = 100 100(0.05) = 5.00
๐=โ [๐ฅ โ๐ (๐ฅ )]=5.9
ฮฃ[xโP(x)]=5.9 ฮฃ[x2โP(x)]=40.2
๐=โ๐2
Find the mean, variance, and standard deviation of the probability distribution.
X P(x) xโP(x) x2 x2โP(x)2 0.15 2(0.15) = 0.30 22 = 4 4(0.15) = 0.604 0.20 4(0.20) = 0.80 42 = 16 16(0.20) = 3.206 0.25 6(0.25) = 1.50 62 = 36 36(0.25) = 9.008 0.35 8(0.35) = 2.80 82 = 64 64(0.35) = 22.40
10 0.05 10(0.05) = 0.50 102 = 100 100(0.05) = 5.00
๐=โ [๐ฅ โ๐ (๐ฅ )]=5.9
ฮฃ[xโP(x)]=5.9 ฮฃ[x2โP(x)]=40.2
๐=โ๐2=โ5.39โ2.32Standard Deviation