Question

You throw a four sided symmetric die, if X denotes the number you get on top you receive 2X dollars. However, to play this game you need to pay 4 dollars to begin with. Let Y denote your win in one throw. Find E(Y) in two different ways. i.e. using the probability distribution function of Y and using E(X)

Answer #1

x

You roll a fair 6-sided die once and observe the result which is
shown by the random variable X. At this point, you can stop and win
X dollars. Or, you can also choose to discard the X dollars you win
in the first roll, and roll the die for a second time to observe
the value Y. In this case, you will win Y dollars. Let W be the
number of dollars that you win in this game.
a)...

A game of chance involves rolling a 15-sided die once. If a
number from 1 to 3 comes up, you win 2 dollars. If the number 4 or
5 comes up, you win 8 dollars. If any other number comes up, you
lose. If it costs 5 dollars to play, what is your expected net
winnings?

n a game of throw the dice, it costs 15 pebbles to throw once.
If you throw a 6, you get 20 pebbles, if you throw a 4 or a 5, you
get 15 pebbles, and if you throw a 1, 2, or 3, you get 10 pebbles.
Let X denote the net winning of pebbles after one throw of the
dice. Show all work with equations
a) What is the probability that your net winning of one throw is...

PROBLEM #2
Suppose you play a game in which a fair 6 sided die is rolled
once. If the outcome of the roll (the number of dots on the side
facing upward) is less than or equal to 4, you are paid as many
dollars as the number you have rolled. Otherwise, you lose as many
dollars as the number you have rolled.
Let X be the profit from the game (or the amount of money won or
lost per...

Let X equal the outcome (1, 2 , 3 or 4) when a fair four-sided
die is rolled; let Y equal the outcome (1, 2, 3, 4, 5 or 6) when a
fair six-sided die is rolled. Let W=X+Y.
a. What is the pdf of W?
b What is E(W)?

On three rolls of a single die, you will lose
$14
if a
6
turns up at least once, and you will win
$6
otherwise. What is the expected value of the game?
Let X be the random variable for the amount won on a single play
of this game.
E(X)equals=____
dollars (Type an integer or a decimal rounded to the nearest
cent as needed.)

a fair die was rolled repeatedly.
a) Let X denote the number of rolls until you get at least 3
different results. Find E(X) without calculating the distribution
of X.
b) Let S denote the number of rolls until you get a repeated
result. Find E(S).

I roll a fair die until I get my first ace. Let X be the number
of rolls I need.
You roll a fair die until you get your first ace. Let Y be the
number of rolls you need.
(a) Find P( X+Y = 8)
HINT: Suppose you and I roll the same die, with me going first.
In how many ways can it happen that X+Y = 8, and what is the
probability of each of those ways?...

Roll a fair four-sided die twice. Let X be the sum of the two
rolls, and let Y be the larger of the two rolls (or the common
value if a tie).
a) Find E(X|Y = 4)
b) Find the distribution of the random variable E(X|Y )
c) Find E(E(X|Y )). What does this represent?
d) Find E(XY |Y = 4)
e) Find the distribution of the random variable E(XY |Y )
f) Explain why E(XY |Y ) = Y...

Suppose that you are offered the following "deal." You roll a
six sided die. If you roll a 6, you win $12. If you roll a 2, 3, 4
or 5, you win $1. Otherwise, you pay $10.
a. Complete the PDF Table. List the X values, where X is the
profit, from smallest to largest. Round to 4 decimal places where
appropriate.
Probability Distribution Table
X
P(X)
b. Find the expected profit. $ (Round to the nearest cent)
c....

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