Question

Suppose that Mr. Warren Buffet and Mr. Zhao Danyang agree to meet at a specified place between 12 pm and 1 pm. Suppose each person arrives between 12 pm and 1 pm at random with uniform probability. What is the distribution function for the length of the time that the first to arrive has to wait for the other?

Answer 1

Answer:  $f(x)=1\ \text{where}\ 12\leq x\leq 13$

Step-by-step explanation:

The probability distribution function for uniform distribution in interval [a,b] is given by :_

$f(x)=\dfrac{1}{b-a}\ \text{where}\ a\leq x\leq b$

Given : Mr. Warren Buffet and Mr. Zhao Danyang agree to meet at a specified place between 12 pm and 1 pm.

Since 1 pm comes after 12 pm, and in 24 hours system we call it as 13 pm.

If each person arrives between 12 pm and 1 pm at random with uniform probability, then the uniform distribution function for this will be :_

$f(x)=\dfrac{1}{13-12}=1\ \text{where}\ 1\leq x\leq 12$

Hence. the distribution function for the length of the time that the first to arrive has to wait for the other will be :-

$f(x)=1\ \text{where}\ 12\leq x\leq 13$