Find the expected value of the probability experiment with outcomes $X_{1}, X_{2}, \ldots$
\[
X_{1}=\$ 10, X_{2}=\$ 4, X_{3}=\$ 2 ; P\left(X_{1}\right)=\frac{3}{8}, P\left(X_{2}\right)=\frac{1}{8}, P\left(X_{3}\right)=\frac{4}{8}
\]
The expected value of the probability experiment is $\$ \square$. (Round your answer to the nearest cent, if necessary.)
Answer
Simplify the fraction to get the final answer: \(\boxed{E(X) = $5.25}\)
Step 1 ：The expected value E(X) of a probability experiment is calculated by multiplying each outcome by its probability and then summing these products. The formula is given by E(X) = X1*P(X1) + X2*P(X2) + X3*P(X3)
Step 2 ：Substitute the given values into the formula: E(X) = $10*(3/8) + $4*(1/8) + $2*(4/8)
Step 3 ：Perform the multiplication: E(X) = $30/8 + $4/8 + $8/8
Step 4 ：Add the fractions: E(X) = $42/8
Step 5 ：Simplify the fraction to get the final answer: \(\boxed{E(X) = $5.25}\)
