If X takes the values 1 and 3 with equal probability, what is Var(X)?

Unlock all questions

This demo includes only 20 questions. Upgrade to access hundreds of questions, flashcards, exam simulations, and disable ads.

Full question bankExam simulationsFlashcards
From $24.99Unlock all

Enhance your understanding of Descriptive Statistics and Probability. Study with interactive questions and detailed explanations. Prepare effectively for your test!

Multiple Choice

If X takes the values 1 and 3 with equal probability, what is Var(X)?

Explanation:
Variance measures how far the values of a random variable tend to spread around its average. For X that can be 1 or 3 with equal probability, first find the mean: μ = (1 + 3) / 2 = 2. Then compute the second moment: E[X^2] = (1^2 + 3^2) / 2 = (1 + 9) / 2 = 5. The variance is E[X^2] − μ^2 = 5 − 2^2 = 5 − 4 = 1. So Var(X) = 1. Since the two possible values are each 1 unit away from the mean, the average squared deviation confirms the same result.

Variance measures how far the values of a random variable tend to spread around its average. For X that can be 1 or 3 with equal probability, first find the mean: μ = (1 + 3) / 2 = 2. Then compute the second moment: E[X^2] = (1^2 + 3^2) / 2 = (1 + 9) / 2 = 5. The variance is E[X^2] − μ^2 = 5 − 2^2 = 5 − 4 = 1. So Var(X) = 1. Since the two possible values are each 1 unit away from the mean, the average squared deviation confirms the same result.

More Multiple Choice Questions
Subscribe

Get the latest from Examzify

You can unsubscribe at any time. Read our privacy policy