1) 4 ballpoint pens are selected without replacement at random from a box that contains 2 blue pens, 3 red pens, and 5 green pens.
If X is the number of blue pens selected and Y is the number of red pens selected

a. Write the “joint probability distribution” of x and y.

b. Find P[(X, Y ) ∈ A], where A is the region
{(x, y)|x + y ≤ 2}.

c. Show that the column and row totals of a Table and give the marginal distribution of X alone and of Y alone

d. Find the conditional distribution of Y, given that X = 1; namely, f (Y|1)=?

e. Use it to determine P(Y = 0 | X = 1).

f. Show that if the random variables X and Y are statistically independent or NOT independent.

A box contains billions of tickets, all labeled either 1, 2, 3, 4, or 5. A simple random sample of 400 tickets is taken; the sample mean is 2.6 and the sample SD is 1. Let μ represent the population mean. Which of the following statements are correct? (More than one statement may be correct.)

A. There is a 68% probability that μ is between 2.55 and 2.65.
B. The interval between 2.55 and 2.65 is a 68% confidence interval for μ.

C. There is a 90% probability that μ is between 2.5 and 2.7.
D. The interval between 2.5 and 2.7 is a 90% confidence interval for μ.

E. The interval between 2.5 and 2.7 is a 95% confidence interval for μ.

F. There is a 95% probability that μ is between 2.5 and 2.7.

1) Consider X a normal random variable with mean 4 and standard deviation 2. Given that P(X<6)=0.841345 , compute P(2<= x <= 6)

2)Consider X a normal random variable with mean 10 and standard deviation 4. Given that P(x>9)=0.598708 and P(x<12)=0.691464 . Compute P(8< x < 11).

You will receive the following cash payments as a retirement settlement: Year 1 2 3 4 5 Amount $10,000 $20,000 $50,000 $50,000 $75,000 In place of the above you are offered a check today for $178,000. Assuming an interest rate of 4%, which would you choose? If an interest rate of 3% was used would this change your selection? Explain.

I am trying to determine operating cash flow for years 1, 2, 3 and 4 for a company who is evaluating a new MRI machine. I calculated the revenue based on # of scans times the net revenue for each scan and got $900,000. Should this figure remain the same for years 2, 3, and 4 or does the neutral inflation rate of 2% need to be added to each?

Also, does depreciation, variable and fixed costs change with the 2% neutral inflation rate? I am thinking that fixed costs and depreciation will not change.

Please answer as soon as possible. 2-4 sentences in fine.

1. Describe the Avalanche Effect in your own words. Give an example of the avalanche effect in cryptographic algorithms.

2. What is a collision in terms of a hash value and what implications does it have for the hash function? Give examples of possible situations.

3. Describe how symmetric and asymmetric key cryptography are different. List one example of symmetric key cryptography and one example of asymmetric key cryptography highlighting any difference and any similarities.

Consider the set of five numbers {0, 2, 4, 6, 8}.

1) Make a list of all possible samples of size 2 that can be drawn from this set of integers. (Sample without replacements, that is, once a number is selected, you don’t put it back in the sample set.)

2) Make a list of all possible sample means for samples of size 2 selected from this set.

3) List the distribution of the sample means and construct a histogram of this distribution.

Bubble Sort is performed on an array with values [6, 1, 2, 0, 5, 4]. What are the array values after two passes of the Bubble Sort? The largest value in the array is moved to the correct location after each pass.

Question 1

Why is testing important?

Question 2

What are the 4 different types of testing activities? What is the purpose of each type?

Question 3

What is the Waterfall methodology?