### Educational Content: Probability Mass Function Using Hypergeometric Distribution#### ScenarioA pharmaceutical company has given 30 subjects a new antihistamine and another 30 subjects a placebo (a pill containing no medicine). From these 60 subjects, 8 are randomly selected for further study. Let the random variable $ X $ denote the number of subjects among the 8 selected who were given the placebo.#### Questions1. **Probability Mass Function (PMF) $ f(x) = P(X = x) $**: - Find and express the PMF. - Sketch the histogram of $ f(x) $.2. **Specific Probability Calculation**: - Find $ P(X = 4) $. What does this number represent?3. **Cumulative Probability**: - Find $ P(X \geq 4) $. What does this number represent? - Find $ P(X \leq 6) $. What does this number represent?#### Solution FrameworkUsing the hypergeometric probability distribution model, the function to determine $ f(x) = P(X = x) $ is expressed as:\[ f(x) = \frac{\binom{30}{x} \binom{30}{8-x}}{\binom{60}{8}} \]To find a specific ordered pair in the probability mass function $ f(x) = P(X = x) $, the probability mass function must be solved for different values of $ x $.- **Probability Mass Function Calculation**: You need to calculate the PMF values manually or using computational resources for specific $ x $ values to explore the distribution.- **Histogram**: You can sketch a histogram of the PMF by plotting $ x $ values against the corresponding $ f(x) $ probabilities.For example:- Calculate $ f(x) $ for specific $ x $ values (0 to 8).- Round to three decimal places.- Pair the $ x $ value with its corresponding probability value in the format $ (x, f(x)) $.Engage with the problem by completing these calculations to understand the distribution of subjects who received the placebo during random selection. This scenario uses the hypergeometric distribution due to the nature of sampling without replacement from two distinct groups.

As per our guidelines we can solve first three subpart and rest can be reposted. Solution-: Let,…

Answered: A pharmaceutical company gives 30…

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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