Suppose I play a gambling game where I either win or lose k dollars. Suppose further that the chance of winning is p = .5. I employ the following strategy to try to guarantee that I win some money. I bet $1; if I lose, I double my bet to $2, if I lose I double my bet again. I continue until I win. Eventually I’m sure to win a bet and net $1 (run through the first few rounds and you’ll see why this is the net). If this really worked casinos would be out of business. Our goal in this problem is to understand the flaw in the strategy. (a) Let X be the amount of money bet on the last game (the one I win). X takes values 1, 2, 4, 8, . . . . Determine the probability mass function for X. That is, find p(2k), where k is in {0, 1, 2, . . . }. (b) Compute E(X). (c) Use your answer in part (b) to explain why the stategy is a bad one.

/in /by

Suppose I play a gambling game where I either win or lose k dollars. Suppose further

that the chance of winning is p = .5.

I employ the following strategy to try to guarantee that I win some money.

I bet $1; if I lose, I double my bet to $2, if I lose I double my bet again. I continue until

I win. Eventually I’m sure to win a bet and net $1 (run through the first few rounds and

you’ll see why this is the net).

If this really worked casinos would be out of business. Our goal in this problem is to

understand the flaw in the strategy.

(a) Let X be the amount of money bet on the last game (the one I win). X takes values

1, 2, 4, 8, . . . . Determine the probability mass function for X. That is, find p(2k), where k

is in {0, 1, 2, . . . }.

(b) Compute E(X).

(c) Use your answer in part (b) to explain why the stategy is a bad one.

You might also like
You are saving to pay for your children’s university costs in 20 years’ time. In the first year, your payment is R3 600, after which your yearly payments increased by R360 each year. If the expected interest rate per year is 10%, the amount that you expect to receive to the nearest rand on the maturity date will be [1] R213 030. [2] R340 380. [3] R412 380. [4] R484 380. [5] none of the above
The monopolistic competitor faces a demand curve given by _Q_ (_p_) = 50_−_5_p_. Its cost function is _C(y_) = 4_y_. What is its optimal level of output and price?
Give the table below Labor total product Average Product Marginal (TP) (AP) Product(MP) 0 0 1 10 2 25 3 45 4 60 5 70 6 70 7 60 8 44 Required 1. Complete the table above by computing AP and MP. 2. Plot in one graph TP, AP and MP. Label graph completely . 3. Indicate the stage of production with its corresponding boundaries.
The study of reality in the broadest sense, an inquiry into the elemental nature of the universe and the things in it, is known as _____. a. metaphysics b. epistemology c. quantum physics d. axiology
The great Greek woman who sang on the beauty of love and nature:
Is mental health treatment becoming less stigmatized?
If All warriors are coward= false Find out the truth value of opposite proposition 1.No Non- coward is non- warrior. 2. No Warriors are non- cowards. 3. Some cowards are not non Warriors.
“Symbolic interactionism provides a ‘micro’ perspective concerning the interrelationships between teachers and learners. Based on social interactions with fellow human beings, a key premise of symbolic interactionism is the assignment of meanings to objects in the world.” Now look at the cartoon below: Before you answer the question, read pages 46– 48ofSoE (2018) on the “principles of symbolic interactionism” and then explain how these principles, in terms of the carton contents, assist us to understand how learners construct meanings through interacting ESC3701/101 41 with and interpreting their teachers’ actions. Also provide an example of this process to substantiate your argument.