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

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

the answer is 31.27mph