Answer to Question #189458 in Statistics and Probability for Harsimran

Question

Scott is juggling multiple assignments for his studies. Currently, he has 4 assignments from 4 different subjects (maths, physics, economics, and history) that he needs to start (and complete). He estimates the number of hours taken to complete each of these assignments follow Exponential distributions.

If the time spent on the individual assignment are independent across different subjects, what is the distribution of the total number of hours he expects to spend on all 4 assignments?

Answer 1

Given,

$\lambda_1=0.3,\lambda=0.3,\lambda_3=0.9 \text{ and } \lambda_4=0.5$

if X~$Exp(\lambda) such that f_x(x)=\lambda e^{-\lambda x}$

In this case total number of hours taken to complete the assignment

      $=\dfrac{1}{\lambda_1}+\dfrac{1}{\lambda_2}+\dfrac{1}{\lambda_3}+\dfrac{1}{\lambda_4}\\[9pt] =\dfrac{1}{0.3}+\dfrac{1}{0.3}+\dfrac{1}{0.9}+\dfrac{1}{0.5}\\[9pt] =3.33+3.33+1011+2\\[9pt] =9.77$