Final answer:
The expected value of X², given the mean of 10 and the standard deviation of 5, is 125.
Step-by-step explanation:
To find the expected value of X2, which is denoted as E(X2), we need to use the information that the mean (μ) of the random variable X is 10 and the standard deviation (σ) is 5. The formula for the expected value of X2 is E(X2) = variance + mean2. The variance is the square of the standard deviation, so in this case, the variance is σ2 = 52 = 25. Plugging in these values, we get E(X2) = 25 + 102 = 25 + 100, which equals 125.