Consider rolling two fair dice one 3-sided the other 5-sided
let x and y be the random variables that denote the numbers on the 3-sided and 5-sided die respectively. assuming x and y are independent find the pdf of the sum.. aka define w=x+y

Since the dice are fair and the rolling are independent, each single outcome has probability 1/15. Every time we choose

We have and , because the dice are fair.

Now we use the assumption of independence to claim that

Now, we simply have to count in how many ways we can obtain every possible outcome for the sum. Consider the attached table: we can see that we can obtain:

This implies that the probabilities of the outcomes of are the number of possible ways divided by 15: we can obtain 2 and 8 with probability 1/15, 3 and 7 with probability 2/15, and 4, 5 and 6 with probabilities 3/15=1/5

i used to know how to do this in 7th but i forget easily

step-by-step explanation: