Joint density functions (gaussian)

[simba_]

Would just like a hand with this question

If X and Y are independent standard Gaussian random variables (that is, independent N(0, 1) 's ) do the following:
(a) Write down the joint probability density function fX_X,Y (x, y) of X and Y .

I know what the gaussian density function looks like. Is it just a matter of multiplying two gaussian distributions together... where u have a σ₁ and σ₂ (do the same with the mean)

 

[statdad]

Any time X, Y are independent continuous random variables their joint density is the product of their individual densities - so yes, all you need to do is multiply the individual densities.