1. If X, Y are lognormal distribution, what the distribution of X/Y?

2. what is the probability of getting 40 or less heads in 100 coin tosses. What distribution is this. With what other distribution can you approximate this. What is the final probability.

3. Which is greater exp((a+b)/2) or (exp(a)+exp(b))/2

4. what is the series expansion of (1/(1-x))

7. If x and y have correlation .9 and y and z have correlation .9 what correlation can we have between x and z.

9. A rabbit can jump one step or two steps a time, there are N steps, write down a formula to give all the possible ways.

10. There is a fair coin, give the expected value of the first two consecutive heads show up.

11. There are 15 horses, the maximum number of horses in a race is 5, how many races are needed to identify the top 3 fastest horses.

12. There are stacks (first in last out), simulate pipe (first in first out), what's the order.

14. which one is the bigger e^PI or PI^e, no calculators, explain how to estimate.

15. you take a grid with n rows and m columns. You start from the lower left corner and you have to go to the upper right corner. You can't neither go down or left. How many possibilities have you ?

16. We play a game. You have a probability p to earn 1 dollars and a probability (1-p) to lose 1 dollar. You start the game with ten dollars.
What is your probability to lose 3) dollars before loosing everything?

17. Let's play a game. I roll a die three times. After each time, you can decide to stop me and you will earn in dollars the number the die gives. What is your strategy? Can your write a program that will compute your expectation for the same game but n rolls? Describe your thoughts.

18. What is the solution of the following equation? x^x^x^x^x^x and so on to the infinity =2

19. In a box, you have two coins. One has two head sides, the other one has on head side and one tail side. You takes one coins and you throw it. You get head. What is the probability to get a head if you throw it again ?

See the attached file.
If X1,X2,..., Xn, are (iid) , from a distribution with mean μ and variance σ^2. Define the sample mean as
Xbar = (X1+X2+...+Xn) / n
(a) Show that the mean and variances of the probability density function of Xbar are given as E(Xbar) = μ
Var(Xbar) = (σ^2)/n
b

1. Five percent of a certain grade of tires wear our before 25,000 miles, and another 5 percent of tires exceed 35,000 miles. Determine the tire reliability at 24,000 miles if wearout is normally distributed.
2. The wearout of a machine part has a lognormaldistribution with s=0.5 and t_med=5,630 hours. What is MTTF?

The demand for electricity in megawatts at peak load on any given day is said to be described by a normal random variable with expected value 90 megawatts and standard deviation 10 megawatts (variance 100 megawatts squared). If this description of the demand for electricity is correct, what generating capacity must be available

The problems need to be done in minitab, and have to include ordered data, rank, (xi-.5/n), z, zi
MAT 332
Problem : Thirty measurements of the time - to - failure of a critical component in an electronics assembly are recorded. Determine which probability density model-Normal, lognormal,

I have several questions about water samples that I am having difficulty with. Please utilize minitab to complete work.
1. Fifty samples of water effluent from a chemical processing facility were measured for a required EPA report. The ppm of suspended solids in each specimen is presented in the following table. (a) Examine

Loebuck Grocery orders milk from a dairy on a weekly basis. The manager of the store has developed the following probabilitydistribution for demand per week (in cases):.........see attached

Decide whether the distribution is a probabilitydistribution. If it is not a probabilitydistribution, identify the property that is not satisfied. (References: example 3 and 4 page 197, end of section exercises 25 - 28 page 202 - 203)
x P(x)
0 0.49
1 0.05
2 0.32
3 0.07
4 0.02

Determine whether each of the following is a proper probabilitydistribution. If it is not, why?
a. X 0 5 10 15 20
P(X) 1/4 1/2 1/3 -1/4 1/4
b. X 0 2 4 6
P(X) 1 1.5 0.3 0.2
c. X 1 2 3
P(X) 1/4 1/2 1/4
d. X -2 3 7

What are the two basic laws of probability? What are the differences between a discrete probabilitydistribution and a continuous probabilitydistribution? Provide at least one example of each type of probabilitydistribution.
Answer