Question

a project is graded on a scale of 1 to 5. if the random variable, x, is the project grade, what is the mean of the probability distribution below? probability distribution

Explanation:

Step1: Identify values and probabilities

Let \(x_1 = 1\), \(P(x_1)=0.1\); \(x_2 = 2\), \(P(x_2)=0.2\); \(x_3 = 3\), \(P(x_3)=0.4\); \(x_4 = 4\), \(P(x_4)=0.2\); \(x_5 = 5\), \(P(x_5)=0.1\).

Step2: Use mean formula for discrete - random variables

The mean \(\mu=\sum_{i = 1}^{n}x_iP(x_i)\), so \(\mu=1\times0.1 + 2\times0.2+3\times0.4 + 4\times0.2+5\times0.1\).

Step3: Calculate each product

\(1\times0.1=0.1\), \(2\times0.2 = 0.4\), \(3\times0.4=1.2\), \(4\times0.2 = 0.8\), \(5\times0.1=0.5\).

Step4: Sum up the products

\(\mu=0.1 + 0.4+1.2 + 0.8+0.5=3\).

Answer:

3