how to check a propriety using r studio I have to check that this propriety  
$Z \sim N(0,1)$ and $U\sim \chi ^{2}(10)$  then   $ Z/\sqrt{U/10} \sim T(10)$
is true using r studio if anyone can help , much appreciate 

One approach could be simulation of thousands of values:


*

*Simulate $Z$ using rnorm 

*Simulate $U$ using rchisq 

*Do the division $Y = Z / \sqrt{U / 10}$

*Simulate the same number of $T$ from the hypothesised $t$-distribution using rt  

*Sort $Y$ and $T$ and plot them against each other - you want to see a diagonal straight line essentially $y=x$ with a little noise; this is visual demonstration  though not a proof that the distributions are the same


You can do similar things with the qqplot function if you know what you are doing        
