An airline estimates that 80% of passengers who reserve the tickets actually show up for the flights. Based on this information, it has to decide how many tickets it will sell for each flight, which is typically more than the number of seats actually available. In the economy section of a particular aircraft, 200 seats are available. The airline sells 225 seats. What is the probability that more passengers will show up than there are seats for?

a. A stock has an annual return of 11 percent and a standard deviation of 44 percent. What is the smallest expected gain over the next year with a probability of 1 percent? (Do not round intermediate calculations. Round the z-score value to 3 decimal places when calculating your answer. Enter your answer as a percent rounded to 2 decimal places.)

b. Does this number make sense?

• Yes

• No

A machine produces coins such that the probability of heads, p, follows a Beta distribution with parameters (α, β) = (1, 1). A coin produced by this machine is picked at random and tossed independently n times. Let Y be the number of heads.

1. (a) Find E[Y ].

2. (b) Write down the pmf for Y (your answer can include unevaluated integrals and

   combination numbers [aka “n choose m” symbols]).

Match the following aqueous solutions with the appropriate letter from the column on the right.
1)

2)

3)

Superhero physics: a) Choose a height between 1.00 miles and 3.00 miles. How fast would a superhero have to throw a ball straight upwards in order for it to rise this high? Give your answer in both m/s and mph. Assume air resistance is negligible, since at these speeds that's as believable as superheroes are. b) Choose a time between 1.00 minutes and 3.00 minutes. How fast would a superhero have to throw a ball straight upwards in order for it to spend this much time in the air (that is, for it to take that much time to return to their hand)? Give your answer in both m/s and mph. Same assumption. c) Without resorting to further calculations, which of these two balls will be in the air longer? Explain your reasoning, explicitly citing evidence. d) Choose one case, (a) or (b), and calculate the time required for the ball to rise halfway to its highest point, and the time to rise from there to the highest point. Check: see next question. e) Why does it take less time to rise halfway to the highest point than to rise the rest of the way?

Consider the following two projects: Cash flows Project A Project B C0 −$ 260 −$ 260 C1 110 138 C2 110 138 C3 110 138 C4 110 a. If the opportunity cost of capital is 10%, which of these two projects would you accept (A, B, or both)? b. Suppose that you can choose only one of these two projects. Which would you choose? The discount rate is still 10%. c. Which one would you choose if the cost of capital is 15%? d. What is the payback period of each project? e. Is the project with the shortest payback period also the one with the highest NPV? f. What are the internal rates of return on the two projects? g. Does the IRR rule in this case give the same answer as NPV? h-1. If the opportunity cost of capital is 10%, what is the profitability index for each project? h-2. Is the project with the highest profitability index also the one with the highest NPV? h-3. Which measure should you use to choose between the projects?

In C++

Write a function called findBestSimScore that takes a genome and a sequence and returns the highest similarity score found in the genome as a double.

Note: the term genome refers to the string that represents the complete set of genes in an organism, and sequence to refer to some substring or sub-sequence in the genome.

• Your function MUST be named findBestSimScore

• Your function should take two parameters in this order:

  • a string parameter for the genome (complete set of genes)

  • a string parameter for the sequence (sub-sequence of the genome)

• Your function should return the highest similarity score as a double.

• Your function should not print anything.

The best similarity scores is [0.0,1.0]

Our sequence is "ACT", which is a string of length 3. That means we need to compare our sequence with all the 3 character long sub-sequences (substrings) in the genome.

Examples:

In mice the allele for black coat color (B) is dominant to the allele for white coat color (b). The allele for long tail (T) is dominant to the allele for short tail (t).

For the same cross: BbTt x bbTt

    a. Using the Probability Method illustrated in lecture, break the complex two-gene cross into two simple single-gene crosses (note that the Probability Method can be used if it is known that the alleles of the different genes Assort Independently)

         b. Show the expected genotypic and phenotypic ratios for each of the simple single-gene crosses.

         c. Using this information, show the calculations for determining the expected number of genotypes and the expected number of phenotypes among the offspring of the        BbTt x bbTt cross.

         d. What is the expected frequency of BbTt offspring from the cross? (Show the calculation using the Product Rule).

         e. What is the expected frequency of white coat, long tail offspring? (Show the calculation using the Product Rule).

         f. Using Branching Diagrams show the Full expected genotypic and phenotypic ratios among offspring of the cross. Include the calculation of the frequency of each genotype or phenotype in the branching diagram.       

For adult men, total cholesterol has a mean of 188 mg/dL and a standard deviation of 43 mg/dL. For adult women, total cholesterol has a mean of 193 mg/dL and a standard deviation of 42 mg/dL. The CDC defines “high cholesterol” as having total cholesterol of 240 mg/dL or higher, “borderline high” as having a total cholesterol of more than 200 but less than 240, and “healthy” as having total cholesterol of 200 or less. A study published in 2017 indicated that about 11.3% of adult men and 13.2% of adult women have high cholesterol. USE EXCEL.

1. An adult woman is randomly selected and her total cholesterol is measured. What is the probability it is in the “borderline high” range?

2. In a study of 45 randomly selected adult men, the number who have high cholesterol is counted. (Assume that 11.3% of men have high cholesterol.)

3. How many of these 45 men do you expect to have high cholesterol?

4. What is the standard deviation for the number of these 45 men that have high cholesterol?

5. What is the probability that at least 10 of these 45 men will have high cholesterol?

We have a bag that contains n red balls and n blue balls. At each of 2n rounds we remove one of the balls from the bag randomly, and place it in one of available n bins. At each round, each one of the balls that remain in the bag is equally likely to be picked, as is each of the bins, independent of the results of previous rounds. Let Nk be the number of balls in the k-th bin after 2n rounds, i.e., after all balls have been placed in the bins.

1. Find the probability that N1=0, i.e., that the first bin is empty after all balls have been removed and placed into bins.

2. What is the PMF pN1(k) of N1?

   (Enter factorials by typing for example fact(n) for n!. Do not worry if the parser does not display correctly; the grader will work independently. If you wish to have proper display, enclose any factorial by parentheses, e.g. (fact(n)).)

3. What is the expected number of empty bins?

4. What is the probability that the ball picked in the third round is red?

5. Let Ri denote the event that i-th ball picked is red. Are the events R1 and R2 independent?

   Yes

   No