Central Limit Theorem question
Suppose that $\lbrace X_i \rbrace$ are IID continuous random variables with the following common pdf:
$$f(x)=\left\{\begin{matrix} 2-2x & 0\leq x\leq1 \\ 0 & else \end{matrix}\right.$$
Let $Z$ be a standard normal random variable. Use the Central Limit Theorem to find the number $a$ so that
$$\lim_{n\rightarrow \infty}P\left ( \frac{1}{n} \sum_{i=1}^{n} X_i\leq\frac{1}{3}+\frac{2}{\sqrt n} \right ) = P(Z\leq a) $$

58
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
1.6K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 757 views
- $10.00
Related Questions
- Calculating the Probability of a Varied Selection in Pet Shop Purchases
- How to adjust for an additional variable.
- How do we describe an intuitive arithmetic mean that gives the following? (I can't type more than 200 letters)
- Probability question
- Bad Beat Jackpot
- foundations in probability
- joint continuous probability function finding covariance
- There are 12 people in a room, where each person holds a card with a 2-digit number. What is the probability that there are at least two people holding cards with identical numbers