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

Explanation:

Step1: Recall the formula for expected value

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

Step2: Calculate each term (y_{i}P(y_{i}))

• For (y = - 16) and (P(Y=-16)=0.4): ((-16)\times0.4=-6.4)
• For (y=-15) and (P(Y = - 15)=0.35): ((-15)\times0.35=-5.25)
• For (y=-14) and (P(Y=-14)=0.08): ((-14)\times0.08=-1.12)
• For (y=-13) and (P(Y=-13)=0.1): ((-13)\times0.1=-1.3)
• For (y=-12) and (P(Y=-12)=0.07): ((-12)\times0.07=-0.84)

Step3: Sum up the terms

(E(Y)=(-6.4)+(-5.25)+(-1.12)+(-1.3)+(-0.84)) (E(Y)=-(6.4 + 5.25+1.12 + 1.3+0.84)) (E(Y)=-14.91)

Answer:

(-14.91)