Let ? be the number that shows up when you roll a fair,
six-sided die, and, let ? = ?^2 − 5? + 6.
a. Find both formats for the distribution of ?. (Hint: tep forms
of probability distributions are CDF and pmf/pdf.)
b. Find F(2.35)
Consider some 8-sided dice. Roll two of these dice. Let X be the
minimum of the two values that appear. Let Y denote the
maximum.
a) Find the joint mass p_X,Y (x,y).
b) Compute p_X│Y (x│y) in all cases. Express your final answer
in terms of a table.
Use for Questions 1-7:
Hector will roll two fair, six-sided dice at the same time. Let
A = the event that at least one die lands with the number 3 facing
up. Let B = the event that the sum of the two dice is less than
5.
1. What is the correct set notation for the event that “at least
one die lands with 3 facing up and the sum of the two dice is less
than 5”?
2....
Use for Questions 1-7: Hector will roll two fair, six-sided dice
at the same time. Let A = the event that at least one die lands
with the number 3 facing up. Let B = the event that the sum of the
two dice is less than 5.
1. What is the correct set notation for the event that “at least
one die lands with 3 facing up and the sum of the two dice is less
than 5”?
2....
If you roll two six-sided dice, what is the probability of
obtaining the following outcomes?
a)2 or 3
b) 6 and 4
c) At least one 5
d) Two of the same number (two 1s, or two 2s, or two 3s,
etc.)
e) An even number on both dice
f) An even number on at least one die
A player pays $ 13 to roll three six-sided balanced dice. If the
sum of the 3 dice is less than 13, then the player will receive a
prize of $ 70. Otherwise, you lose the $13.
a. Find the expected value of profit.
Exercise 7-12: Roll a pair of fair 3-sided dice. Let F denote
the number of dots on the first die and let T denote the total
number of dots. Determine the Cov(F,T).
1. Three six-sided dice are rolled. Let X be the sum of the
dice. Determine the range of X and compute P(X = 18) and P(X ≤
4).
2. An urn contains 5 red balls and 3 green balls. (a) Draw 3 balls
with replacement. Let X be the number of red balls drawn. Determine
the range of X and compute P(X = 3) and P(X 6= 1). (b) Draw 3 balls
without replacement. Let Y be the number of...
. Three Dice of a Kind
Consider the following game: You roll six 6-sided dice
d1,…,d6 and you win if some number appears 3 or
more times. For example, if you roll:
(3,3,5,4,6,6)
then you lose. If you roll
(4,1,3,6,4,4)
then you win.
What is the probability that you win this game?
Consider a six-sided fair dice. Complete the following tables
for this die:
Number on the dice
Number of times it appears on the dice
Relative frequency of seeing that number
1
2
3
4
5
6
Total
This is the entire question, does not say how many times the
dice is thrown