Question

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

Explanation:

Step1: Recall the formula for expected value

The formula for the expected value \(E(Z)\) of a discrete random variable is \(E(Z)=\sum_{i}z_{i}P(z_{i})\), where \(z_{i}\) are the values of the random variable and \(P(z_{i})\) are their corresponding probabilities.

Step2: Calculate each product

• For \(z = - 5\) and \(P(-5)=0.25\): \((-5)\times0.25=-1.25\)
• For \(z = - 4\) and \(P(-4)=0.39\): \((-4)\times0.39=-1.56\)
• For \(z = - 3\) and \(P(-3)=0.12\): \((-3)\times0.12=-0.36\)
• For \(z = - 2\) and \(P(-2)=0.04\): \((-2)\times0.04=-0.08\)
• For \(z = - 1\) and \(P(-1)=0.08\): \((-1)\times0.08=-0.08\)
• For \(z = 0\) and \(P(0)=0.12\): \(0\times0.12 = 0\)

Step3: Sum up the products

$$
LATEXBLOCK0
$$

Answer:

\(-3.33\)