uniform probability density function mathematical expression I am helping my daughter with her high school probability homework and it is shocking how much basic stat/probability knowledge I have lost! Appreciate some help with the following question:
The total time to process a loan application is uniformly distributed between 5 and 14 days.
A) Write a mathematical expression for the probability density function and sketch it.
Thinking about it logically, if it is a uniform distribution between 5 and 14 days, each "day" has a .10% probability. Also a uniform distribution sketch will just be a straight horizontal line (at .10%) with vertical lines at 5 and 14. 
What would the mathematical expression be though? Is it just $x \rightarrow \frac{1}{(14-5)}$?
B) What is the probability that the loan app will be processed in 10 days or less?
so we are trying to find $P(5\leq X \leq 10)$. formula should be:
$$P(5 \leq X \leq 10)=\frac{x2-x1}{b-a}\\
x2=10, x1=5, a=5, b=14\\
\frac{10-5}{14-5} = 56\%
$$
Am I close?? Thank you for any help!
 A: 
The total time to process a loan application is uniformly distributed between 5 and 14 days.
A) Write a mathematical expression for the probability density function and sketch it.
Thinking about it logically, if it is a uniform distribution between 5 and 14 days, each "day" has a .10% probability. Also a uniform distribution sketch will just be a straight horizontal line (at .10%) with vertical lines at 5 and 14. 

Yeap.  Uniform means all the same.

What would the mathematical expression be though? Is it just $x\to \frac{1}{(14−5)}$  ?

Close.  For a discrete uniform distribution in the interval $\{a .. b\}$ then $f(x)=\dfrac{1}{b-a\color{red}{+1}}$
So for uniform distribution over 10 days $\mathcal U\{5,6,7,8,9,10,11,12,13,14\}$ it is: $$f(x) = \frac{1}{14-5+1} = \frac 1 {10}$$

B) What is the probability that the loan app will be processed in 10 days or less?
so we are trying to find $P(5≤X≤10)$ . formula should be: 
  $P(5≤X≤10)=\frac{x_2−x_1}{b−a} \quad x_2=10,x_1=5,a=5,b=14
\\ =\frac{10−5}{14−5} =56\%$ 
Am I close?? Thank you for any help!

Close.  $$\mathsf P(5\leq X\leq 10) = \frac{10-5+1}{14-5+1} = \frac{6}{10} = 60\%$$
