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Suppose student Ana is running for a charity and asks her friend to chip in the donation. Suppose each friend donates independently, and the donated value T is a random variable with the following probability density: c ti € [5, 10] dollars p(T₁ = ti) = { t € [35, 40] dollars.

Suppose student Ana is running for a charity and asks her friend to chip in the donation. Suppose each friend donates independently, and the donated value T is a random variable with the following probability density: c ti € [5, 10] dollars p(T₁ = ti) = { t € [35, 40] dollars.

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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Suppose student Ana is running for a charity and asks her friend to chip in the donation. Suppose each friend donates independently, and the donated value \( T_i \) is a random variable with the following probability density: \[ p(T_i = t_k) = \begin{cases} c & t_i \in [5, 10] \text{ dollars} \\ c & t_i \in [35, 40] \text{ dollars} \\ 0 & \text{otherwise} \end{cases} \] Let's assume \( T_i \)'s are mutually independent and each donation is a continuous random variable given they're using electronic transfer. Ana requested from 150 friends for the donation. Let \( X \) be the total amount in dollars Ana collected from these 150 friends. You need to simplify for this problem.
Transcribed Image Text:Suppose student Ana is running for a charity and asks her friend to chip in the donation. Suppose each friend donates independently, and the donated value \( T_i \) is a random variable with the following probability density: \[ p(T_i = t_k) = \begin{cases} c & t_i \in [5, 10] \text{ dollars} \\ c & t_i \in [35, 40] \text{ dollars} \\ 0 & \text{otherwise} \end{cases} \] Let's assume \( T_i \)'s are mutually independent and each donation is a continuous random variable given they're using electronic transfer. Ana requested from 150 friends for the donation. Let \( X \) be the total amount in dollars Ana collected from these 150 friends. You need to simplify for this problem.
### Statistical Question Analysis 1. **Variance Calculation:** - **Question:** What would the variance of \( T_i - T_j \) be assuming \( i \neq j \)? - **Input Box:** A space is provided to enter the variance value, expressed as a number with two significant figures. 2. **Probability Calculation:** - **Question:** What is the probability the absolute difference between two donors' contributions is less than 9 dollars? - **Input Box:** A space is provided for entering the probability, expressed as a number with two significant figures. Each section includes a help icon (represented by a question mark) next to the input fields, possibly to provide additional guidance or clarification on how to compute the respective answers.
Transcribed Image Text:### Statistical Question Analysis 1. **Variance Calculation:** - **Question:** What would the variance of \( T_i - T_j \) be assuming \( i \neq j \)? - **Input Box:** A space is provided to enter the variance value, expressed as a number with two significant figures. 2. **Probability Calculation:** - **Question:** What is the probability the absolute difference between two donors' contributions is less than 9 dollars? - **Input Box:** A space is provided for entering the probability, expressed as a number with two significant figures. Each section includes a help icon (represented by a question mark) next to the input fields, possibly to provide additional guidance or clarification on how to compute the respective answers.
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