Question

the table below shows the probability distribution of a random variable z. what is the mean of the probability distribution? write your answer as a decimal.

Explanation:

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

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

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

• For $z = - 12$ and $P(z)=0.1$: $(-12)\times0.1=-1.2$
• For $z=-11$ and $P(z) = 0.11$: $(-11)\times0.11=-1.21$
• For $z=-10$ and $P(z)=0.01$: $(-10)\times0.01=-0.1$
• For $z=-9$ and $P(z)=0.18$: $(-9)\times0.18=-1.62$
• For $z=-8$ and $P(z)=0.09$: $(-8)\times0.09=-0.72$
• For $z=-7$ and $P(z)=0.51$: $(-7)\times0.51=-3.57$

Step3: Sum up all the terms

$$
LATEXBLOCK0
$$

Answer:

$-8.42$