### Probability and Statistics Quiz**Question:**A box contains 8 marbles: 3 red, 4 blue, and 1 green. We draw without replacement from the box 4 times. Let $X$ be the number of red marbles drawn out. Is $X$ a binomial random variable?**Answer Options:**1. Yes.2. No.3. Are we done yet? ;-) This is not the answer!### Explanation:This question explores the concept of a binomial random variable in probability and statistics. For a variable to be binomial, the following conditions must be met:1. **Fixed Number of Trials:** The experiment is repeated for a fixed number of trials.2. **Two Possible Outcomes:** Each trial has exactly two outcomes – success and failure.3. **Constant Probability:** The probability of success is the same for each trial.4. **Independent Trials:** Each trial is independent of the others.When drawing marbles without replacement, the trials are not independent since the probability changes after each draw. Hence, in this scenario, $X$ cannot be modeled as a binomial random variable even though it initially might seem to fit the binomial criteria.### Detailed Analysis:- **Fixed Number of Trials:** Yes, there are 4 draws.- **Two Possible Outcomes:** If success is defined as drawing a red marble, then yes, each draw results in either a red marble (success) or not (failure).- **Constant Probability:** No, because once a marble is drawn, it is not replaced, altering the probability of drawing another red marble.- **Independent Trials:** No, because the draws affect each other.So, the correct answer is:**2) No.**(Note: Option 3 is a playful option and not a valid answer.)

Answered: A box contains 8 marbles: 3 red, 4…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A box contains 8 marbles: 3 red, 4 blue, and 1 green. We draw without replacement from the box 4 times. Let X be the number of red marbles drawn out. Is X a binomial random variable? 1) Yes. 2) No. 3) Are we done yet? ;-) This is not the answer!