the table below shows the probability distribution of a random variable z. what is the expected value of z…

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.

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.

Answer

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_iP(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_iP(z_i))

  • For (z = - 5) and (P(-5)=0.27): ((-5)\times0.27=-1.35)
  • For (z=-4) and (P(-4) = 0.09): ((-4)\times0.09=-0.36)
  • For (z=-3) and (P(-3)=0.36): ((-3)\times0.36=-1.08)
  • For (z=-2) and (P(-2)=0.16): ((-2)\times0.16=-0.32)
  • For (z=-1) and (P(-1)=0.12): ((-1)\times0.12=-0.12)

Step3: Sum up the terms

(E(Z)=-1.35+( - 0.36)+(-1.08)+(-0.32)+(-0.12)) [ \begin{align*} E(Z)&=-(1.35 + 0.36+1.08+0.32 + 0.12)\ &=-(1.71+1.08+0.32+0.12)\ &=-(2.79+0.32 + 0.12)\ &=-(3.11+0.12)\ &=-3.23 \end{align*} ]

Answer:

(-3.23)