Question

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

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:

\(-14.91\)