Question

Find the expected value of X using the table below.

X

P(X)

0

0.4

1

0.3

─1

0.3

Answer 1

To find the expected value \( E(X) \) of a random variable \( X \) given its probability distribution, we use the formula:

\[
E(X) = \sum (x \cdot P(X = x))
\]

Where \( x \) represents the possible values of the random variable \( X \), and \( P(X = x) \) is the probability of each value.

Given the table you provided:

\[
\begin{array}{|c|c|}
\hline
X & P(X) \\
\hline
0 & 0.4 \\
1 & 0.3 \\
-1 & 0.3 \\
\hline
\end{array}
\]

We calculate the expected value as follows:

1. For \( x = 0 \):
\[
0 \cdot P(X=0) = 0 \cdot 0.4 = 0
\]

2. For \( x = 1 \):
\[
1 \cdot P(X=1) = 1 \cdot 0.3 = 0.3
\]

3. For \( x = -1 \):
\[
-1 \cdot P(X=-1) = -1 \cdot 0.3 = -0.3
\]

Now, we sum these results:
\[
E(X) = 0 + 0.3 - 0.3 = 0
\]

Therefore, the expected value of \( X \) is

\[
\boxed{0}
\]