If X and Y are independent random variables with means E[X] = 2 and E[Y] = 3, what is the expected value of XY?Review LaterE[XY] = 5E[XY] = 6E[XY] = 7E[XY] = 8

Break Down the Problem

1. Identify the given values: We have two independent random variables, X and Y, with means $E[X] = 2$ and $E[Y] = 3$.
2. Determine the formula: For independent random variables, the expected value of their product is the product of their expected values, i.e., $E[XY] = E[X] \cdot E[Y]$.

Relevant Concepts

1. Independence of Random Variables: For independent random variables $X$ and $Y$, we know that: $E[XY] = E[X] \cdot E[Y]$

Analysis and Detail

1. Substituting the Values:

   • Substituting the means: $E[XY] = E[X] \cdot E[Y] = 2 \cdot 3$

2. Perform the Calculation: $E[XY] = 6$

Verify and Summarize

1. Verification:
   • Independent random variables mean we can multiply their expected values. Thus, our calculation checks out.
2. Summary: The expected value of the product of independent random variables $X$ and $Y$ is confirmed to be 6.

Final Answer

$E[XY] = 6$