Why I get high observation when I generate data from t-distribution in R I want to generate 200 samples from t-distribution with the degree of freedom=1 and sample size is 10 and in R
I use this code
set.seed(1234)
B <- matrix(rt(10*200, 1), 200)

But when I see the sample number 167 (B[167,]) I found this high number 602.1691029
And this strange thing in the t-distribution. What is wrong here?


And this strange thing in the t-distribution.

No, it isn't, not with $1$ degree of freedom.
The tails in the Cauchy are so heavy even its mean is undefined (not finite). Very, very large deviations happen reasonably often -- the more values you generate the bigger the largest-magnitude value will tend to be; indeed with the Cauchy it grows roughly linearly with sample size (e.g. $\text{median}({\max_i}(|X_{i}|))$ increases approximately in proportion to $n$; with $2000$ standard Cauchy values the median of the distribution of the largest-magnitude one is over $1800$ and the median of the distribution of the second-largest-magnitude observation is over $750$).
Note that $P(|X|\geq 602)\approx 0.001$. If you generate $2000$ of them you expect roughly about $2$ of those observations to be at least that large in magnitude.
Rather than being surprised to see one of that size, you would often see even larger ones.

What is wrong here?

Nothing, this is typical. You might like to read more about the Cauchy and other t distributions with low d.f.
https://en.wikipedia.org/wiki/Cauchy_distribution
https://en.wikipedia.org/wiki/Student's_t-distribution
A number of posts on site here discuss interesting properties of the Cauchy ($t_1$) distribution.
