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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]

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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]Create a column of x∙P(x)

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(x)2 0.154 0.206 0.258 0.3510 0.05

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]Create a column of x∙P(x)

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(x)2 0.15 2(0.15) = 0.304 0.206 0.258 0.3510 0.05

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]Create a column of x∙P(x)

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(x)2 0.15 2(0.15) = 0.304 0.20 4(0.20) = 0.806 0.258 0.3510 0.05

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]Create a column of x∙P(x)

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]Create a column of x∙P(x)

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]Create a column of x∙P(x)

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]Create a column of x∙P(x)

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]

Sum the column of x∙P(x)

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]

Sum the column of x∙P(x)

Σ[x∙P(x)]=5.9

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]=5.9

Σ[x∙P(x)]=5.9

Mean

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]=5.9

Σ[x∙P(x)]=5.9

𝜎 2=∑ [𝑥2 ∙𝑃 (𝑥 )]−𝜇2

Create a column of x2

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]=5.9

Σ[x∙P(x)]=5.9

𝜎 2=∑ [𝑥2 ∙𝑃 (𝑥 )]−𝜇2

Create a column of x2

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]=5.9

Σ[x∙P(x)]=5.9

𝜎 2=∑ [𝑥2 ∙𝑃 (𝑥 )]−𝜇2

Create a column of x2

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]=5.9

Σ[x∙P(x)]=5.9

𝜎 2=∑ [𝑥2 ∙𝑃 (𝑥 )]−𝜇2

Create a column of x2

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]=5.9

Σ[x∙P(x)]=5.9

𝜎 2=∑ [𝑥2 ∙𝑃 (𝑥 )]−𝜇2

Create a column of x2

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]=5.9

Σ[x∙P(x)]=5.9

𝜎 2=∑ [𝑥2 ∙𝑃 (𝑥 )]−𝜇2

Create a column of x2

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]=5.9

Σ[x∙P(x)]=5.9

𝜎 2=∑ [𝑥2 ∙𝑃 (𝑥 )]−𝜇2

Create a column of x2

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]=5.9

Σ[x∙P(x)]=5.9

𝜎 2=∑ [𝑥2 ∙𝑃 (𝑥 )]−𝜇2

Create a column of x2∙P(x)

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(x) x2 x2∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]=5.9

Σ[x∙P(x)]=5.9

𝜎 2=∑ [𝑥2 ∙𝑃 (𝑥 )]−𝜇2

Create a column of x2∙P(x)

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(x) x2 x2∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]=5.9

Σ[x∙P(x)]=5.9

𝜎 2=∑ [𝑥2 ∙𝑃 (𝑥 )]−𝜇2

Create a column of x2∙P(x)

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(x) x2 x2∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]=5.9

Σ[x∙P(x)]=5.9

𝜎 2=∑ [𝑥2 ∙𝑃 (𝑥 )]−𝜇2

Create a column of x2∙P(x)

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(x) x2 x2∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]=5.9

Σ[x∙P(x)]=5.9

𝜎 2=∑ [𝑥2 ∙𝑃 (𝑥 )]−𝜇2

Create a column of x2∙P(x)

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(x) x2 x2∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]=5.9

Σ[x∙P(x)]=5.9

𝜎 2=∑ [𝑥2 ∙𝑃 (𝑥 )]−𝜇2

Create a column of x2∙P(x)

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(x) x2 x2∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]=5.9

Σ[x∙P(x)]=5.9

𝜎 2=∑ [𝑥2 ∙𝑃 (𝑥 )]−𝜇2

Create a column of x2∙P(x)

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(x) x2 x2∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]=5.9

Σ[x∙P(x)]=5.9

𝜎 2=∑ [𝑥2 ∙𝑃 (𝑥 )]−𝜇2

Sum the column of x2∙P(x)

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(x) x2 x2∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]=5.9

Σ[x∙P(x)]=5.9

𝜎 2=∑ [𝑥2 ∙𝑃 (𝑥 )]−𝜇2

Sum the column of x2∙P(x)Σ[x2∙P(x)]=40.2

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(x) x2 x2∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]=5.9

Σ[x∙P(x)]=5.9 Σ[x2∙P(x)]=40.2Variance

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(x) x2 x2∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]=5.9

Σ[x∙P(x)]=5.9 Σ[x2∙P(x)]=40.2

𝜎=√𝜎2

Find the mean, variance, and standard deviation of the probability distribution.

X P(x) x∙P(x) x2 x2∙P(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

𝜇=∑ [𝑥 ∙𝑃 (𝑥 )]=5.9

Σ[x∙P(x)]=5.9 Σ[x2∙P(x)]=40.2

𝜎=√𝜎2=√5.39≈2.32Standard Deviation