A newly built casino is introducing a new gamble. Since this game is extremely new, the casino is offering a free play to everyone (no money or chips needed to gamble) so that all players get a sense of this new game. The game is played with the following rules

There are 3 decks of 20 cards each on the table:
• Deck A contains 20 red cards numbered 1–20.
• Deck B contains 10 red cards numbered 21–30 and 10 blue cards.
• Deck C contains 5 red cards numbered 31–35 and 15 blue cards.
Each of the 3 decks is shuffled, and 1 card is drawn from each deck. These 3 cards are shuffled and put
face down on the table, making a new pile of 3 cards. Let R be the number of red cards among these 3
cards.
a. Compute the expected value and the variance of R.

Parts b–d describe three different ways in which you could learn that the pile of 3 cards formed above
(with 1 card from each of the 3 decks) has 2 red cards. In each case, determine the probability that
the third card in the pile is also red. Note that these three parts are all independent—for example, the
information given in part b does not carry over to parts c or d.

b. The 3 cards in the new pile are turned over one at a time. The first card is the red 32, and the
second card is the red 5. What is the probability that the third card in the pile is also red?
c. The 3 cards in the new pile are turned over one at a time, but you only see the color on each card
(not the number). The first two cards flipped over are red. What is the probability that the third
card in the pile is also red?
d. You ask a friend to look at the 3 cards in the pile without showing you the cards. You ask them,
“Are there at least 2 red cards in the pile?” They confirm that yes, there are at least 2 reds in the
pile. What is the probability that all 3 cards are red?

1. . Let X1, . . . , Xn, Y1, . . . , Yn be mutually independent random variables, and Z = 1 n Pn i=1 XiYi . Suppose for each i ∈ {1, . . . , n}, Xi ∼ Bernoulli(p), Yi ∼ Binomial(n, p). What is Var[Z]?

2. There is a fair coin and a biased coin that flips heads with probability 1/4. You randomly pick one of the coins and flip it until you get a heads. Let X be the number of flips you need. Compute E[X] and Var[X].

3. A man has a set of n keys, one of which fits the door to his apartment. He tries the keys randomly, throwing away each ill-fitting key that he tries until he finds the key that fits. That is, he chooses keys randomly from among those he has not yet tried. This way he is sure to find the right key within n tries. Let T be the number of times he tries keys until he finds the right key. Write closed-form expressions for E[T] and Var[T]. Hint: Write T as a linear combination of indicator variables.

4. (a) What is the probability that a 5-card poker hand has at least three spades? (b) What upper bound does Markov’s Theorem give for this probability? (c) What upper bound does Chebyshev’s Theorem give for this probability?

5. A random variable X is always strictly larger than −100. You know that E[X] = −60. Give the best upper bound you can on P(X ≥ −20).

6. Suppose that we roll a standard fair die 100 times. Let X be the sum of the numbers that appear over the 100 rolls. Use Chebyshev’s inequality to bound P[|X − 350| ≥ 50].

7. Given any two random variables X and Y , by the linearity of expectation we have E[X −Y ] = E[X]−E[Y ]. Prove that, when X and Y are independent, Var[X − Y ] = Var[X] + Var[Y].

Annuity payments. The Federal Reserve Bank of St. Louis has files listing historical interest rates on its website www.stlouisfeld.org. Find the link for “FRED” (Federal Reserve Economic Data). You will find a listing for the Bank Prime Loan Rate. The file lists the monthly prime rates since January 1949 (1949.01). What is the most recent prime rate? What is the highest prime rate over this period? If you buy a house for $150,000 at the current prime rate on a 30-year mortgage with monthly payments, how much are your payments? If you had purchased the house at the same price when the prime rate was at its highest, what would your monthly payments have been?

You are a consultant to a large manufacturing corporation considering a project with the following net after-tax cash flows (in millions of dollars): Years from Now After-Tax CF 0 –36 1–9 12 10 24 The project's beta is 1.5. Assuming rf = 4% and E(rM) = 12% a. What is the net present value of the project? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.) Net present value 24.72 million b. What is the highest possible beta estimate for the project before its NPV becomes negative? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Highest possible beta value

Coronado Company reports the following operating results for the month of August: sales $310,000 (units 5,000); variable costs $214,000; and fixed costs $71,000. Management is considering the following independent courses of action to increase net income.

Compute the net income to be earned under each alternative.

1. Increase selling price by 10% with no change in total variable costs or sales volume.

2. Reduce variable costs to 57% of sales.

3. Reduce fixed costs by $24,000.

Which course of action will produce the highest net income? select an alternative with the highest net income
                                                           Alternative 3 /. Alternative 1/. Alternative 2

java programming

write a program with arrays to ask the first name, last name, middle initial, IDnumber and 3 test scores of 10 students.

calculate the average of the 3 test scores. show the highest class average and the lowest class average. also show the average of the whole class.

please use basic codes and arrays with loops the out put should look like this:

sample output

first name middle initial last name    ID    test score1 test score2 test score3

dhdh d djddj. 3456 20    80. 67

the class average is 80

the highest class average is80

the lowest class average is 80

please use printf to format the output

You are a consultant to a large manufacturing corporation considering a project with the following net after-tax cash flows (in millions of dollars): Years from Now After-Tax CF 0 –36 1–9 12 10 24 The project's beta is 1.5. Assuming rf = 4% and E(rM) = 12% a. What is the net present value of the project? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.) Net present value million b. What is the highest possible beta estimate for the project before its NPV becomes negative? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Highest possible beta value

CarrieMovies = {"Titanic":3.5, "Mean Girls":4.9, "Finding Nemo":4.7, "Wonder Woman": 4.3}

LeslieMovies = {"Clueless": 3.2, "Spy Kids":4.1, "Black Panther":5.0}

def topMovie():

return

CarriesFav = topMovie(CarrieMovies)

LesliesFav = topMovie(LeslieMovies)

print("Carrie's Fav Movie: ",CarriesFav)

print("Leslie's Fav Movie: ",LesliesFav)

_Complete the function topMovie(). This program is not complete.

The purpose of the function is to determine the title of the highest rated movie in a dictionary. The starter file defines two dictionaries of favorite films and their associated ratings. The function should be dynamic and able to return the title of the highest rated movie for any dictionary passed to it!

output is:

Carrie's Fav Movie: Mean Girls
Leslie's Fav Movie: Black Panther