Question

We play a game where we throw a coin at most 4 times. If we get 2 heads at any point, then we win the game. If we do not get 2 heads after 4 tosses, then we loose the game. For example, HT H, is a winning case, while T HT T is a losing one. We define an indicator random variable X as the win from this game.

You make a decision that after you loose 3 times, not necessarily consecutively but overall, then you quit playing. On average, how many times you will play this game before quitting?

Answer #1

You play a coin flip game where you win NOTHING if the coin
comes up heads or win $1,000 if the coin comes up tails. Assume a
fair coin is used. Which of the following is TRUE?
Group of answer choices
a. A risk-seeking person would be willing to accept a cash
payment of $500 to forgo (i.e. pass up) playing the game.
b. A risk neutral person might accept a cash payment of $400 to
forgo (i.e. pass up)...

Suppose that you get the opportunity to play a coin flipping
game where if your first flip is a “head”, then you get to flip
five more times; otherwise you only get to flip two more times.
Assuming that the coin is fair and that each flip is
independent, what is the expected total number of “heads”?

After losing few bucks on a roulette game at a casino company
over the last weekend, Craig was about leaving for studying CFA
exam. However, to retain customers in the store, the casino company
was offering a promotion: a free cash of $140 or a chance to win
the prize of a coin game. The coin game is described as
follows:
The prize of the game depends on an unbiased coin you toss. If
the heads appear, you get $200....

A player is given the choice to play this game. The player flips
a coin until they get the first Heads. Points are awarded based on
how many flips it took:
1 flip (the very first flip is Heads): 2 points
2 flips (the second flip was the first Heads): 4 points
3 flips (the third flip was the first Heads): 8 points
4 flips (the fourth flip was the first Heads): 16 points
and so on. If the player...

We play a game with a deck of 52 regular playing cards, of which
26 are red and 26 are black. They’re randomly shuffled and placed
face down on a table. You have the option of “taking” or “skipping”
the top card. If you skip the top card, then that card is revealed
and we continue playing with the remaining deck. If you take the
top card, then the game ends; you win if the card you took was
revealed...

1. Let X be the number of heads in 4 tosses of a fair coin.
(a) What is the probability distribution of X? Please show how
probability is calculated.
(b) What are the mean and variance of X?
(c) Consider a game where you win $5 for every head but lose $3
for every tail that appears in 4 tosses of a fair coin. Let the
variable Y denote the winnings from this game. Formulate the
probability distribution of Y...

Consider a game in which a coin will be flipped three times. For
each heads you will be paid $100. Assume that the coin comes up
heads with probability ⅔.
a. Construct a table of the possibilities and probabilities in
this game. The table below gives you a hint on how to do this and
shows you that there are now eight possible outcomes. (3
points)
b. Compute the expected value of the game. (2 points)
c. How much would...

A fair coin is tossed three times. What is the probability
that:
a. We get at least 1 tail
b. The second toss is a tail
c. We get no tails.
d. We get exactly one head.
e. You get more tails than heads.

Consider the following game. You flip an unfair coin, with P(H)
= 1/4 and P(T) = 3/4, 100 times. Every time you flip a heads you
win $8, and every time you flip a tails you lose $3. Let X be the
amount of money you win/lose during the game. Justify your answers
and show all work. Compute E(X) andCompute V (X).

(a)Assuming that we toss a in-balanced coin for 100 times, and
we get 40 heads from our experiment. Assuming that the relative
frequency is just the true probability for tossing to get a head.
Then we want to know:
Probability for getting a head:
Expected variance if tossing 70 times:
(b)Given a poisson distribution with expectation 4, so the standard
deviation of this distribution should be

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