the table below shows the probability distribution of a random variable x.\nwhat is the mean of the…

Explanation:

Step1: Recall the formula for the mean of a probability distribution

The mean $\mu$ of a probability distribution is given by $\mu=\sum_{i}x_{i}P(x_{i})$, where $x_{i}$ are the values of the random variable and $P(x_{i})$ are their corresponding probabilities.

Step2: Calculate each term $x_{i}P(x_{i})$

• For $x = 3$ and $P(3)=0.2$: $3\times0.2=0.6$
• For $x = 4$ and $P(4)=0.2$: $4\times0.2 = 0.8$
• For $x = 5$ and $P(5)=0.2$: $5\times0.2=1$
• For $x = 6$ and $P(6)=0.4$: $6\times0.4 = 2.4$

Step3: Sum up the terms

$\mu=0.6 + 0.8+1+2.4$

Answer:

$4.8$