Homework 4

	Student A
Full Name	Ido Fang Bentov
ID	CLASSIFIED
Email	CLASSIFIED

---

---

Question 1

Let and be two independent random variables. Define a new random variable as . Find the PMF of .

Solution:
Since and are independent, the PMF of is given by the the convolution of the PMFs of and :

Plugging in the PMFs of and , we get:

Question 2

I roll a fair die repeatedly until a number larger than is observed. If is the total number of times that I roll the die find for .

Solution:
The probability of rolling a number larger than is .
Assuming the number of rolls is , according to the geometric distribution, the probability of getting one successful roll after rolls is