Given the following probability distribution, what is the expected value of the random variable X? $$\begin{array} { c c }
X & P ( X ) \
100 & .10 \
150 & .20 \
200 & .30 \
250 & .30 \
300 & .10 \
\text { Sum } & 1.00
\end{array}$$
A)175
B)150
C)200
D)205

Question

Given the following probability distribution, what is the expected value of the random variable X? $$\begin{array} { c c } 
X & P ( X ) \
100 & .10 \
150 & .20 \
200 & .30 \
250 & .30 \
300 & .10 \
\text { Sum } & 1.00
\end{array}$$
A)175
B)150
C)200
D)205

Quizplus · Accepted Answer

The expected value (E[X]) of a random variable X is calculated by summing the products of each outcome and its corresponding probability: E[X] = Σ [X * P(X)]. For this distribution, E[X] = (100 * .10) + (150 * .20) + (200 * .30) + (250 * .30) + (300 * .10) = 10 + 30 + 60 + 75 + 30 = 205.

Given the Following Probability Distribution, What Is the Expected Value XP(X)100.10150.20200.30250.30300.10 Sum 1.00\begin{array} { c c } X & P ( X ) \\100 & .10 \\150 & .20 \\200 & .30 \\250 & .30 \\300 & .10 \\\text { Sum } & 1.00\end{array}X100150200250300 Sum ​P(X).10.20.30.30.101.00​

Given the Following Probability Distribution, What Is the Expected Value $\begin{array} { c c } X & P ( X ) \\100 & .10 \\150 & .20 \\200 & .30 \\250 & .30 \\300 & .10 \\\text { Sum } & 1.00\end{array}$