Let x1~ exp(1) and x2 ~ exp(1) be independent and identically-distributed exponential random variables with rate 1.

let: y = x1 + x2 , z = x1 − x2

(a) what is the cdf of x1?

(b) what is the joint pdf of (x1, x2)?

(c) what is the joint pdf of (y, z)?

(d) what is the marginal pdf of z?

Lance lived in portugal and brazil for a total of 14 months to learn portuguese. he learned an average of 130 new words per month when he lived in portugal, and an average of 150 new words per month when he lived in brazil. in total he learned 1920 new words. write a system of equations to represent the situation. use x to represent portugal, and y to represent brazil

If i have one apple and give you the apple, how many apples do i have?

Ijust need to see how to do this. so you don’t have to answer all of them just a step by step explanation of one.