a project is graded on a scale of 1 to 5. if the random variable, x, is the project grade, what is the mean…
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 0.2 0.4 1 3
Answer
Explanation:
Step1: Identify values and probabilities
Let (x_1 = 1), (p_1=0.1); (x_2 = 2), (p_2 = 0.2); (x_3=3), (p_3 = 0.4); (x_4 = 4), (p_4=0.2); (x_5 = 5), (p_5=0.1)
Step2: Apply mean - formula
The formula for the mean (\mu) of a discrete probability distribution is (\mu=\sum_{i = 1}^{n}x_ip_i). So (\mu=x_1p_1+x_2p_2+x_3p_3+x_4p_4+x_5p_5). [ \begin{align*} \mu&=(1\times0.1)+(2\times0.2)+(3\times0.4)+(4\times0.2)+(5\times0.1)\ &=0.1 + 0.4+1.2 + 0.8+0.5\ &=3 \end{align*} ]
Answer:
3