Answer: [tex]f(x)=1\ \text{where}\ 12\leq x\leq 13[/tex]
Step-by-step explanation:
The probability distribution function for uniform distribution in interval [a,b] is given by :_
[tex]f(x)=\dfrac{1}{b-a}\ \text{where}\ a\leq x\leq b[/tex]
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 :_
[tex]f(x)=\dfrac{1}{13-12}=1\ \text{where}\ 1\leq x\leq 12[/tex]
Hence. the distribution function for the length of the time that the first to arrive has to wait for the other will be :-
[tex]f(x)=1\ \text{where}\ 12\leq x\leq 13[/tex]
