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e table below gives the probability distribution for a discrete random variable X. X 0 1 p 0.32 0.16 ? A. What is the missing number to make the probability distribution valid? The missing number is B. Find P(X = 0). C. Find P(X ≤ 2). GI 2 3 4 5 0.18 0.14 0.05 9.

e table below gives the probability distribution for a discrete random variable X. X 0 1 p 0.32 0.16 ? A. What is the missing number to make the probability distribution valid? The missing number is B. Find P(X = 0). C. Find P(X ≤ 2). GI 2 3 4 5 0.18 0.14 0.05 9.

MATLAB: An Introduction with Applications
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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**Probability Distribution for a Discrete Random Variable** The table below gives the probability distribution for a discrete random variable \( X \). | \( X \) | 0 | 1 | 2 | 3 | 4 | 5 | |---------|-----|-----|-----|-----|-----|-----| | \( p \) | 0.32| 0.16| ? | 0.18| 0.14| 0.05| **A. What is the missing number to make the probability distribution valid?** To find the missing number, recall that the sum of all probabilities must equal 1. The missing number is ⬜. **B. Find \( P(X = 0) \).** The probability that \( X \) equals 0 is \( P(X = 0) \). \(P(X = 0)\) is ⬜. **C. Find \( P(X \leq 2) \).** This is the sum of the probabilities for \( X \) equals 0, 1, and 2. \( P(X \leq 2) \) is ⬜. **D. Find \( P(X \geq 2) \).** This is the sum of the probabilities for \( X \) equals 2, 3, 4, and 5. \( P(X \geq 2) \) is ⬜. **Explanation of Diagrams** The table above organizes the information into a clear format, listing the possible values of \( X \) on the top row and their corresponding probabilities \( p \) directly below them. Each column represents a pair \((X, p)\), where \( X \) is the value the random variable can take, and \( p \) is the probability of \( X \) taking that value. This is a standard way to display a discrete probability distribution, making it easy to see and sum the probabilities to ensure they total to 1.
Transcribed Image Text:**Probability Distribution for a Discrete Random Variable** The table below gives the probability distribution for a discrete random variable \( X \). | \( X \) | 0 | 1 | 2 | 3 | 4 | 5 | |---------|-----|-----|-----|-----|-----|-----| | \( p \) | 0.32| 0.16| ? | 0.18| 0.14| 0.05| **A. What is the missing number to make the probability distribution valid?** To find the missing number, recall that the sum of all probabilities must equal 1. The missing number is ⬜. **B. Find \( P(X = 0) \).** The probability that \( X \) equals 0 is \( P(X = 0) \). \(P(X = 0)\) is ⬜. **C. Find \( P(X \leq 2) \).** This is the sum of the probabilities for \( X \) equals 0, 1, and 2. \( P(X \leq 2) \) is ⬜. **D. Find \( P(X \geq 2) \).** This is the sum of the probabilities for \( X \) equals 2, 3, 4, and 5. \( P(X \geq 2) \) is ⬜. **Explanation of Diagrams** The table above organizes the information into a clear format, listing the possible values of \( X \) on the top row and their corresponding probabilities \( p \) directly below them. Each column represents a pair \((X, p)\), where \( X \) is the value the random variable can take, and \( p \) is the probability of \( X \) taking that value. This is a standard way to display a discrete probability distribution, making it easy to see and sum the probabilities to ensure they total to 1.
Here is the transcription of the image which can be used on an educational website: --- ### Probability Questions E. Find \( P(X < 2) \). \[ \boxed{} \] F. Find \( P(X > 2) \). \[ \boxed{} \] --- (Note: The image does not include any graphs or diagrams, only text and input boxes on a screen above a keyboard on a laptop. If there were any graphs or diagrams, they would be described in detail.)
Transcribed Image Text:Here is the transcription of the image which can be used on an educational website: --- ### Probability Questions E. Find \( P(X < 2) \). \[ \boxed{} \] F. Find \( P(X > 2) \). \[ \boxed{} \] --- (Note: The image does not include any graphs or diagrams, only text and input boxes on a screen above a keyboard on a laptop. If there were any graphs or diagrams, they would be described in detail.)
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