Question

the table below shows the probability distribution of a random variable x. 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 \(\mu=\sum_{i}x_{i}P(x_{i})\), 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 \(x = - 15\) and \(P(x)=0.38\): \((-15)\times0.38=-5.7\)
• For \(x = - 14\) and \(P(x)=0.1\): \((-14)\times0.1=-1.4\)
• For \(x = - 13\) and \(P(x)=0.17\): \((-13)\times0.17=-2.21\)
• For \(x = - 12\) and \(P(x)=0.06\): \((-12)\times0.06=-0.72\)
• For \(x = - 11\) and \(P(x)=0.22\): \((-11)\times0.22=-2.42\)
• For \(x = - 10\) and \(P(x)=0.07\): \((-10)\times0.07=-0.7\)

Step3: Sum up the terms

\(\mu=-5.7+( - 1.4)+(-2.21)+(-0.72)+(-2.42)+(-0.7)\)

$$
LATEXBLOCK0
$$

Answer:

\(-13.15\)