# probability

1. ### Definition of random variable with respect to event space

It is given that: We toss two dice with sample space Ω = {(i, j), 1 ≤ i, j ≤ 6} and the σ-algebra is generated by the events Ak = {(i,j) : max(i,j) = k} (k = 1, . . . , 6). Show that whereas X1(i, j) = max(i, j) is a random variable in the corresponding probability space, X2(i, j) = i + j is...
2. ### Conditional Monthly Risk Calibration for a trading model

Hi, I have a trading system with a portfolio of assets (long and shorts) with daily market returns. I want to overlay a risk management to my trading system that calibrate my portfolio positions on a daily basis so that a monthly portfolio loss of lets say 20% only occurs 1% of the time...
3. ### Row problem with mandatory empty seats

Here is the exact question: Suppose that 39 students (you being one of them) are randomly seated in a long row of 120 seats. How likely is it that you will not have a direct neighbor? What I've understood: that one the side you can only have one seat with no neighbor next to you and one...
4. ### Racing

Hi all, I need some help with some statistical work: So, I am trying to understand how I can transform time into probability. I have 2 teams playing a game for 10 minutes. One team scores 1 pt per each minute and the other team takes 1,5 minutes in average to score one point. I want...
5. ### Bionomial Probability Distributions

51% of men consider themselves professional baseball fans. You randomly select 10 men and ask each if he considers himself a professional baseball fan. Find the probability that the number who consider themselves baseball fans is (a) exactly five, (b) at least six, and (c) less than four (a)...
6. ### Probability Questions - Cannot seem to figure out

I have been working on this problem for a few days now and cannot seem to at least find a formula or example in my book that works. Any help would be very much appreciated, thanks! In 2009, according to a Harris Interactive poll, 52% of American college graduates have Facebook accounts...
7. ### Game Probability Question

Hi, I am playing a game. I win with an 88% chance and lose with 12% probability. If I have won 20 games in a row what is the probabilty that I will lose the next game. If you can figure out the answer and provide also the calculation logic that would be great. Thanks B
8. ### Gage R&R results to usable data

This is for my thesis & i'm stumped. Please help. A Gage R&R was done comparing two inspection tools to each other. These tools measure the section modulus of wood, which is used to calculate the SI and whether or not we replace the wood. The measurements using the tools were normalize, that...
9. ### Calculation of expected values for chi-squared test

Folks I need to work out the probability that a set of survey results occurred by chance, and I intend to use a chi-squared test. However, I haven't studied mathematics formally since I was 16, and I need someone to confirm whether my calculations of expected values are accurate and, if not...
10. ### Probability of more than 5 responses surveying two locations with different response

You are looking for people between 16 to 23 years to answer a survey. Assume houses on First Street, based on copious amounts of empty beer bottles in front yards and your past experience, has a chance of yielding 16 to 23 year olds to answer your survey of 20% per house. Houses on Second...
11. ### Bayes' formula question help

One percent of population cannot drive even if they try very very hard, but everyone applies for the driving license. The driving test fails those who cannot drive with a chance of 97%, but because the test has to be strict, it fails those who drive well with a probability of 3%. How likely it...
12. ### Working out standard deviation for three random variables with different sized ranges

X = {1,2,3,4,5,6}, Y = {1,2,3,4}, Z = {2,4,6,8}. The question is: work out standard deviation of A = 2S-1, where S = the sum of the three random variables. I know that E(X) = 3.5, E(Y) = 2.5, E(Z) = 5 Var(X) = 2.916, Var(Y) 1.25, Var(Z) = 5 Now in order to find out the standard...
13. ### calculating $E(Y)$

suppose X is random variable non negative with Distribution function F_{X}(x) and Y is random variable with Distribution function G_{Y}(t)=1-E(e^{-tX}) ,0\leq t . how can i calculate E(Y)
14. ### How to calculate probability of two samples

Hello everyone, Just need advice how to calculate probability of two samples in a 2 x 4 table. so say i have two groups (brown haired people and blonde haired people) and the columns are 4 levels on a game. I have the counts for the numbers of people that got to each level. How do I...
15. ### Conditional probability of functions. Small question

Hey, i was just looking at a question where the question is calculate: P( B(t) =< x| x=B(s) ). That is, calculate the probability that B(t) is less than or equal to x given that x is equal to B(s). Here B(t) is a brownian motion, but my question is not related to this. I understand the...
16. ### Determine the risk (probability) of meeting forecasted demand

Hi, I'm doing a project for a car company for my final year studying Industrial Engineering. The company forecast demand 4 months ahead but, according to history data, the company rarely meets the forecast demand. The Supply Chain Department asked me to develop a model that would, with...
17. ### Dice probability question

What are the odds of rolling 2d6(2 6-sided dice) three times and getting two 3s? How about rolling 4 times; 5 times? I know rolling a 2d6 has a 5.56% chance of landing a 3. How do I calculate the chances of that happening twice in 3/4/5 rolls?
18. ### bayes's theorem and conditional probability question

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19. ### Dice probability with limited reroll

Hello, I'm having difficulty understanding this problem and I was wondering if someone had an answer. Let n = \text{Number of dice} = 3 p_s = \text{Single die success probability (when the face is 3 or more)} = \frac{1}{2} k = \text{Number of successful die} \in 0, 1, 2, 3 P(n, k...
20. ### Probability of most expensive item automatically being purchased

Hi all, many thanks for any input on this perplexing problem: If a sporting good store offers a coupon as follows: Free soccer ball OR free T-shirt OR free Hat And their POS system automatically credits the highest purchase priced item to the individual if it is in their shopping...