Mean of a discrete random variable.ppt

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The document shows the steps to calculate the mean of a probability distribution. A table lists the possible values (X) of a random variable, their respective probabilities (P(x)), and the product of each x and P(x). These products are summed to obtain 1.7, which is equal to the mean (μ) of the probability distribution.

Example 6: Find the mean of the probability
distribution.
X P(x)
0 0.2
1 0.3
2 0.2
3 0.2
4 0.1

Example 6: Find the mean of the probability
distribution.
𝜇 = 𝑥 ∙ 𝑃(𝑥)X P(x)
0 0.2
1 0.3
2 0.2
3 0.2
4 0.1

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Example 6: Find the mean of the probability
distribution.
X P(x)
0 0.2
1 0.3
2 0.2
3 0.2
4 0.1
𝜇 = 𝑥 ∙ 𝑃(𝑥)
Create a column of x∙P(x)

Example 6: Find the mean of the probability
distribution.
X P(x) x∙P(x)
0 0.2
1 0.3
2 0.2
3 0.2
4 0.1
𝜇 = 𝑥 ∙ 𝑃(𝑥)
Create a column of x∙P(x)

Example 6: Find the mean of the probability
distribution.
X P(x) x∙P(x)
0 0.2 0(0.2) = 0
1 0.3
2 0.2
3 0.2
4 0.1
𝜇 = 𝑥 ∙ 𝑃(𝑥)
Create a column of x∙P(x)

Example 6: Find the mean of the probability
distribution.
X P(x) x∙P(x)
0 0.2 0(0.2) = 0
1 0.3 1(0.3) = 0.3
2 0.2
3 0.2
4 0.1
𝜇 = 𝑥 ∙ 𝑃(𝑥)
Create a column of x∙P(x)

Example 6: Find the mean of the probability
distribution.
X P(x) x∙P(x)
0 0.2 0(0.2) = 0
1 0.3 1(0.3) = 0.3
2 0.2 2(0.2) = 0.4
3 0.2
4 0.1
𝜇 = 𝑥 ∙ 𝑃(𝑥)
Create a column of x∙P(x)

Example 6: Find the mean of the probability
distribution.
X P(x) x∙P(x)
0 0.2 0(0.2) = 0
1 0.3 1(0.3) = 0.3
2 0.2 2(0.2) = 0.4
3 0.2 3(0.2) = 0.6
4 0.1
𝜇 = 𝑥 ∙ 𝑃(𝑥)
Create a column of x∙P(x)

Example 6: Find the mean of the probability
distribution.
X P(x) x∙P(x)
0 0.2 0(0.2) = 0
1 0.3 1(0.3) = 0.3
2 0.2 2(0.2) = 0.4
3 0.2 3(0.2) = 0.6
4 0.1 4(0.1) = 0.4
𝜇 = 𝑥 ∙ 𝑃(𝑥)
Create a column of x∙P(x)

Example 6: Find the mean of the probability
distribution.
X P(x) x∙P(x)
0 0.2 0(0.2) = 0
1 0.3 1(0.3) = 0.3
2 0.2 2(0.2) = 0.4
3 0.2 3(0.2) = 0.6
4 0.1 4(0.1) = 0.4
𝜇 = 𝑥 ∙ 𝑃(𝑥)
Sum the column of x∙P(x)

Example 6: Find the mean of the probability
distribution.
X P(x) x∙P(x)
0 0.2 0(0.2) = 0
1 0.3 1(0.3) = 0.3
2 0.2 2(0.2) = 0.4
3 0.2 3(0.2) = 0.6
4 0.1 4(0.1) = 0.4
𝜇 = 𝑥 ∙ 𝑃(𝑥)
Sum the column of x∙P(x)
Σ[x∙P(x)]=1.7

Example 6: Find the mean of the probability
distribution.
X P(x) x∙P(x)
0 0.2 0(0.2) = 0
1 0.3 1(0.3) = 0.3
2 0.2 2(0.2) = 0.4
3 0.2 3(0.2) = 0.6
4 0.1 4(0.1) = 0.4
𝜇 = 𝑥 ∙ 𝑃(𝑥) = 1.7
Σ[x∙P(x)]=1.7

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1. Example 6: Find the mean of the probability distribution. X P(x) 0 0.2 1 0.3 2 0.2 3 0.2 4 0.1

2. Example 6: Find the mean of the probability distribution. 𝜇 = 𝑥 ∙ 𝑃(𝑥)X P(x) 0 0.2 1 0.3 2 0.2 3 0.2 4 0.1

3. Example 6: Find the mean of the probability distribution. X P(x) 0 0.2 1 0.3 2 0.2 3 0.2 4 0.1 𝜇 = 𝑥 ∙ 𝑃(𝑥) Create a column of x∙P(x)

4. Example 6: Find the mean of the probability distribution. X P(x) x∙P(x) 0 0.2 1 0.3 2 0.2 3 0.2 4 0.1 𝜇 = 𝑥 ∙ 𝑃(𝑥) Create a column of x∙P(x)

5. Example 6: Find the mean of the probability distribution. X P(x) x∙P(x) 0 0.2 0(0.2) = 0 1 0.3 2 0.2 3 0.2 4 0.1 𝜇 = 𝑥 ∙ 𝑃(𝑥) Create a column of x∙P(x)

6. Example 6: Find the mean of the probability distribution. X P(x) x∙P(x) 0 0.2 0(0.2) = 0 1 0.3 1(0.3) = 0.3 2 0.2 3 0.2 4 0.1 𝜇 = 𝑥 ∙ 𝑃(𝑥) Create a column of x∙P(x)

7. Example 6: Find the mean of the probability distribution. X P(x) x∙P(x) 0 0.2 0(0.2) = 0 1 0.3 1(0.3) = 0.3 2 0.2 2(0.2) = 0.4 3 0.2 4 0.1 𝜇 = 𝑥 ∙ 𝑃(𝑥) Create a column of x∙P(x)

8. Example 6: Find the mean of the probability distribution. X P(x) x∙P(x) 0 0.2 0(0.2) = 0 1 0.3 1(0.3) = 0.3 2 0.2 2(0.2) = 0.4 3 0.2 3(0.2) = 0.6 4 0.1 𝜇 = 𝑥 ∙ 𝑃(𝑥) Create a column of x∙P(x)

9. Example 6: Find the mean of the probability distribution. X P(x) x∙P(x) 0 0.2 0(0.2) = 0 1 0.3 1(0.3) = 0.3 2 0.2 2(0.2) = 0.4 3 0.2 3(0.2) = 0.6 4 0.1 4(0.1) = 0.4 𝜇 = 𝑥 ∙ 𝑃(𝑥) Create a column of x∙P(x)

10. Example 6: Find the mean of the probability distribution. X P(x) x∙P(x) 0 0.2 0(0.2) = 0 1 0.3 1(0.3) = 0.3 2 0.2 2(0.2) = 0.4 3 0.2 3(0.2) = 0.6 4 0.1 4(0.1) = 0.4 𝜇 = 𝑥 ∙ 𝑃(𝑥) Sum the column of x∙P(x)

11. Example 6: Find the mean of the probability distribution. X P(x) x∙P(x) 0 0.2 0(0.2) = 0 1 0.3 1(0.3) = 0.3 2 0.2 2(0.2) = 0.4 3 0.2 3(0.2) = 0.6 4 0.1 4(0.1) = 0.4 𝜇 = 𝑥 ∙ 𝑃(𝑥) Sum the column of x∙P(x) Σ[x∙P(x)]=1.7

12. Example 6: Find the mean of the probability distribution. X P(x) x∙P(x) 0 0.2 0(0.2) = 0 1 0.3 1(0.3) = 0.3 2 0.2 2(0.2) = 0.4 3 0.2 3(0.2) = 0.6 4 0.1 4(0.1) = 0.4 𝜇 = 𝑥 ∙ 𝑃(𝑥) = 1.7 Σ[x∙P(x)]=1.7

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