probabaility

1. Automatic Parking Problem Solving

I have a mathematical problem hope if you can help in solve it. Consider that we have an Automatic Parking Garage contains 900 units , each unit can contains just one car. The Garage open 24 hours per day , 7 days per week (24*7). The working day will divide into three parts 1- (8:00 am - 3:00...
2. Need help figuring out probability that an instrument will strike a price in a given

Hello, I have a formulas for figuring out probability the price of will reach a strike price within T days. Now what I need help with is figuring out the probability price will strike a strike price with in a given (T) minutes, or (T) hours, instead of just days, how would I go about solving...
3. Continuous Random Variable Proof

Question: If X is a random variable for which P(X \geq 0)=0 and |\mu_x|<\infty, show that P(X<\mu t) \geq 1 - \frac{1}{t} for every t \geq 1. My TA told me to use the following information: \mu=\int_{-\infty}^{\infty}(x(f(x))dx Since P(X \geq 0)=0: \mu=\int_{0}^{\infty}(x(f(x))dx...
4. Density curve

=1/2xbasexheight cannot work it out??? tried so many time
5. Game of bridge and probability

Hello Members, There are 4 players in game of bridge and thirteen cards out of 52 cards are to be distributed.(A deck of bridge cards are arranged in a four suits of 13 each. The 4 suits are called spades, clubs, hearts, diamonds. The last 2 are red, the first 2 are black. Cards of the same...

7. How does one find the Co-variance of U and V?

I know one must use the formulas above to get the answer however I just do not see the pattern that is suppose to be present. If anyone knows how to use the formula to finish the problem it would be much appreciated if you can show how you got to that result. (Wondering)
8. Confusion about joint and conditional probability

A person has 16 headaches (H) in 30 days, means P(H) = 16/30 = 0.53 The person tracked his Stress Level and Lack of Sleep for those 30 days. It is assumed that High Stress (HS) and Lack of Sleep (LoS) are independent events and might be responsible for his headaches. Based on the tracked data...
9. More Probability help required! Thanks in advance!

The mean number of times per year that a group's members take domestic flights for personal reasons is 6. Assume a Poisson distribution and calcluate the results to 4 decimal places. a) What is the probability that a member does not take a domestic flight this year? b) What is the probability...
10. Example of Beta distribution

Could anyone show a simple example of Beta distibution [1].How does the normalization takes place in beta distribution?I would like an answer that explains the concepts in laymen terms.(Worried) [1]: https://en.wikipedia.org/wiki/Beta_distribution
11. probabaility of having certain number of parents in a committee

A committee of 5 members is formed from 6 parents , 2 teachers, and a principal, In how many ways, can this committee be formed if the committee consists of not more than 4 parents? my working is 1 parent + 2 parents + 3 parents +4 parents which is (6C1 x 8C4) + (6C2 x 7C3) +(6C3x 6C2)+ (6C4...
12. Probability question

How do I do this question? The NSW government offers generous scholarships to encourage students to take up study and commit to working in areas where it determines there are shortages. In 2014 the government granted 100 scholarships to the University of Western Sydney. UWS was to grant 70 of...
13. covariance for sum of random variables of pipes

It was found that the demand for A and B pipes were normally distributed with means oF 75.4L/min and 69.4L/min respectively, and standard deviations of 2.54L/min and 1.95L/min respectively. It was also found that the standard deviation of the difference in demand on A and B was 1.74L/min...
14. Binomial probability

A candy shop makes 5000 candies per day, of which 30% have strawberry flavour. Every Sunday, Jack buys 15 candies randomly. Determine the probability that on a given Sunday, there will be at least 6 candies with strawberry flavour that Jack has bought. 1−Binomcdf(15,0.3,5) ? Am I right? In...
15. Help for $U = T^2$ has an $F$ distribution with 1 numerator and $v$ denominator degre

If $T$ has a $t$ distribution with $v$ degrees of freedom, then $U = T^2$ has an $F$ distribution with 1 numerator and $v$ denominator degrees of freedom. First, I set $$T = \frac{Z}{\sqrt(W/v)}$$, where $T$ is t distribution with $v$ df, W is a chi-squared distributed variable with v df, and...
16. Understanding the setup for the probability that $Ax^2+Bx+C$ has real roots if A, B,

Suppose that $A, B,$ and $C$ are independent random variables, each being uniformly distributed over $(0,1)$. What is the probability that $Ax^2 + Bx + C$ has real roots? First, I set $P(B^2 - 4AC \ge 0)$ Then I am told that \begin{align} \int_0^1 \int_0^1 \int_{\min\{1, \sqrt{4ac}\}}^1 1...
17. Looking for approach to prove $\bar{x}$ and $s$ are independent for t-statistic

Given t statistic $t = \frac{\bar{x} - \mu}{s/\sqrt(n)}$ Could anyone mention the approach to prove $\bar(x)$ and $s$ are independent...you do not need to prove it...just tell the methods. As I knew that there are several methods to find $\bar(x)$ and $s$ are independent One approach that I...
18. Coins and Dice Probabaility

You have a fair coin. Your friend has a fair die you flip your coin 10 times. Your friend rolls his die 15 times. What is the probability that you get "heads" exactly the same number of times your friend gets "3" or "5". Leave your answer in the form of a summation. No need to simplify! Assume...