Distribution of Random variables

I am trying distribution of a random variable X=Y1+Y2+……+Yn where Y1,Y2…,Yn are i.i.d. uniformly distributed random variables? What can you conclude from the resulting PDF?

[Sasi]

Consider the random variables 𝑌1 = 𝑋1 and 𝑌2 = 𝑋1 + 𝑋2 in answering the following: 7.1 If 𝑋1 and 𝑋2 are uniform random variables, plot the scatter diagram of 𝑌2 vs. 𝑌1 using MATLAB. What do you notice?

[Dyuman Joshi]

@Sasi what have you tried yet?

See Walter's answer below for a hint.

Answer 1

[Walter Roberson]

n = 2000;
histogram( sum(rand(1000, n)), n/10 )

What do you observe?

[Chung Di]

That's the thing I am confused. I already done the coding. Actually I do not understand this part: What can you conclude from the resulting PDF?

[Walter Roberson]

If you

histogram(sum(rand(5000,2000)),200)

then what distribution does the shape look like? Here, the 5000 is the number of variables being added together.

Hint: "central limit"