Hello for this question I'm getting really confused on how to do/calculate the table and was wondering if you would be able to do a step by step solution on how to find the value at each probability please and thank you. ### Educational Website Content---**Title: Probability Distribution of Side Effects in Drug Research Study****Introduction:**In a drug research study, individuals suffering from arthritis participate in testing an experimental pain relief medication. It is given that 40% of all individuals taking the new drug experience a particular side effect. For each individual, let \( X \) be a random variable where \( X = 1 \) indicates the presence of the side effect and \( X = 0 \) indicates its absence. We are to determine the probability distribution for the number of people experiencing the side effect when \( n = 3 \) individuals participate in the study.**Task:**Find the probability distribution of the proportion of participants (among the three) who experience the side effect. This involves listing all possible values for the sample proportion as well as their chances of occurring.**Probability Distribution Table:**| \( x \) | \( P(x) \) ||---------|--------------|| 0 | || 1 | || 2 | || 3 | |*(Type integers or decimals. Do not round.)***Instructions:**- Identify and calculate all possible outcomes in which 0, 1, 2, or all 3 individuals experience the side effect.- Use the given probability (0.4 for experiencing the side effect) and its complement (0.6 for not experiencing the side effect) for calculations involving binomial probabilities.- Fill in the probability values for each \( x \) in the table provided.**Conclusion:**Understanding the probability distribution helps in assessing the likelihood of different outcomes in a sample, which is essential for evaluating the potential effects of the medication on a larger scale. **Note:**Ensure accurate calculations by applying appropriate probability formulas, possibly the binomial probability formula, to determine \( P(x) \) values for each scenario.--- **Graphical Explanation:**In this scenario, there are no graphs or diagrams included. The task involves constructing a table for probability distribution based on calculations.

We have given that p = 40% = 0.40n = 3 Since here we have given that random variable takes only two values either 0 or 1. Thus it is Bernoulli random variable. The sum of Bernoulli random variable is a binomial distribution Here we will use binomial distribution because probability of success is fixed out of fixed number of trials The PMF of the Binomial distribution isP(X= x) = (nCx ) px (1 - p)n-x x = 0,1,2... i) The probability distribution when x = 0 is follows P(X=0) = (3C0 ) 0.400(1 - 0.40)3-0 P(X=0) = 0.216 ii) The probability distribution when x = 1 is follows P(X=1) = (3C1 ) 0.401(1 - 0.40)3-1 P(X= 1) = 0.432 iii) The probability distribution when x = 2 is follows P(X=2) = (3C2 ) 0.402(1 - 0.40)3-2 P(X=2) = 0.288iv) The probability distribution when x = 2 is follows P(X=3) = (3C3 ) 0.403(1 - 0.40)3-3 P(X=3) = 0.064 Thus, we complete the table as: x P(x) 0 0.216 1 0.432 2 0.288 3 0.064

Math

Statistics

As part of a drug research study, individuals suffering from arthritis take an experimental pain relief medication. Suppose that 40% of all individuals who take the new drug experience a certain side effect. For a given individual, let X be either 1 or 0, depending on whether he or she experienced the side effect or not, respectively. Complete parts a through c below. a. If n = 3 people take the drug, find the probability distribution of the proportion who will experience the side effect. (Hint: List all possible values for the sample proportion and their chances of occurring.) P(x) X 0 1 2 3 (Type integers or decimals. Do not round.)

As part of a drug research study, individuals suffering from arthritis take an experimental pain relief medication. Suppose that 40% of all individuals who take the new drug experience a certain side effect. For a given individual, let X be either 1 or 0, depending on whether he or she experienced the side effect or not, respectively. Complete parts a through c below. a. If n = 3 people take the drug, find the probability distribution of the proportion who will experience the side effect. (Hint: List all possible values for the sample proportion and their chances of occurring.) P(x) X 0 1 2 3 (Type integers or decimals. Do not round.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Question

Hello for this question I'm getting really confused on how to do/calculate the table and was wondering if you would be able to do a step by step solution on how to find the value at each probability please and thank you.

### Educational Website Content

---

**Title: Probability Distribution of Side Effects in Drug Research Study**

**Introduction:**
In a drug research study, individuals suffering from arthritis participate in testing an experimental pain relief medication. It is given that 40% of all individuals taking the new drug experience a particular side effect. For each individual, let \( X \) be a random variable where \( X = 1 \) indicates the presence of the side effect and \( X = 0 \) indicates its absence. We are to determine the probability distribution for the number of people experiencing the side effect when \( n = 3 \) individuals participate in the study.

**Task:**
Find the probability distribution of the proportion of participants (among the three) who experience the side effect. This involves listing all possible values for the sample proportion as well as their chances of occurring.

**Probability Distribution Table:**

| \( x \) | \( P(x) \) |
|---------|--------------|
| 0 | |
| 1 | |
| 2 | |
| 3 | |

*(Type integers or decimals. Do not round.)*

**Instructions:**
- Identify and calculate all possible outcomes in which 0, 1, 2, or all 3 individuals experience the side effect.
- Use the given probability (0.4 for experiencing the side effect) and its complement (0.6 for not experiencing the side effect) for calculations involving binomial probabilities.
- Fill in the probability values for each \( x \) in the table provided.

**Conclusion:**
Understanding the probability distribution helps in assessing the likelihood of different outcomes in a sample, which is essential for evaluating the potential effects of the medication on a larger scale.

**Note:**
Ensure accurate calculations by applying appropriate probability formulas, possibly the binomial probability formula, to determine \( P(x) \) values for each scenario.

---

**Graphical Explanation:**
In this scenario, there are no graphs or diagrams included. The task involves constructing a table for probability distribution based on calculations.

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