# probability distribution

1. ### Probability of a multiple variables sum

Hi everyone, I’m coming here for really advance statistic/probability advice. I would like to know the probability of a variable TAU_total such as TAU_total=TAU1+TAU2+….+TAU129. The variables TAUi are independent of each other. For each one of them, I have a sample of 20,000 values which you...
2. ### How to get amount to pay in order to be fair

If a man purchases a raffle ticket, he can win a first price of $50,000 or a second price of$20, 000 with probabilities 0.001 and 0.003. What should be a fair price to pay for the ticket?
3. ### Help with homework. Decision rule to minimise a type 1 error of a sample mean, with probability unknown

Question link: My answer: 1a) To minimize, you make the decision rule being, reject null hypothesis if x-bar is more than 1, or less than 0. Since there is 0 probability of happening, you never make a type 1 error b) 1 - p-cubed c) 0.9 cubed = 0.729 However, I don't exactly understand the...
4. ### Modelling continuous measurements

In the attachment from a set of notes, a brief description of how we describe a continuous measurement is described. I have a few basic questions regarding this, any assistance would be appreciated: Questions: I think the motivation for defining \DeltaW_n is to define it as the error per...
5. ### Estimating probability of critical value

Hello everyone, Once we get a critical value (for example 4.5) how can we estimate the probability of having a value higher than 4.5 if the probability distribution is not normally distributed? I leave in attachment a picture of the histogram that I get. Thank you very much for all the...

7. ### How to evaluate Mean and Variance of Min Function??

Detail is Given in Image attach
8. ### Poisson Distribution using probabilities

If X follows a poisson distribution where P(X=1)=0.4,P(X=2)=0.6, what is the value of P(X=0)? How will I solve this question?
9. ### Shared car usage

Given a pool of C cars available to use by P people, the arrival rate of drivers to borrow cars is r, and the average trip time is t, how often will there be zero cars available for use?
10. ### Could someone verify my logic for managing probability distributions in an experiment

I'm not well versed in stats lingo, but am hoping my logic in the concepts here makes sense and is correct. Often in my work (measuring electrical responses of cells) I take of more than one independent measure per sample, such as the time to an event occurring, along with the size of that...
11. ### PDF of (nearly) collinear variables

My question is motivated by a problem with estimation by maximum likelihood. In simple terms, I want to estimate a parameter \beta and have three variables, X, Y and Z, such that Z = X+Y. Using all three variables is pointless and the joint pdf is singular. Now, suppose that instead of Z I have...
12. ### Probability distribution of combinations

Hi to everybody! I would ask an advice on an analysis that I want to do. I have n=69 balls, within 69, 17 are black balls, 29 white balls, 22 red balls and 1 yellow balls. How can I compute a probability distribution of all possible combinations in r=7 positions, considering that could...
13. ### Probability distribution of all possible combinations

Hi to everybody! I would ask an advice on an analysis that I want to do. I have n=69 balls, within 69, 17 are black balls, 29 white balls, 22 red balls and 1 yellow balls. How can I compute a probability distribution of all possible combinations in r=7 positions, considering that could...
14. ### Quantile prediction?

Here is my situation. I am trying to predict the 'entire' distribution of the dependent variable, not just the mean( or conditional mean). Does it then make sense to seprateley predict quantiles of this variable to learn about the new predicted CDF? I intend to use this CDF as one input (say...
15. ### How to determine distribution with no parameters

I'm confused by this question and I was hoping for some guidance some one to point me in the right direction Let X1.........Xn be a random sample from a population with mean μ, that is E(Xi)=μ for all 1≤i≤n. Define Yi=1 if Xi<μ and Yi=0 otherwise a) Determine the distribution of...
16. ### Class Distribution, Boosted Models (gbm) Probability Scores

All, Problem: I need help to better understand the probability scores that come from the result of a decision tree model. Specifically, I'm using the gbm package from R to create Generalized Boosted Regression Models, but the results I see are common across various ensemble classification...
17. ### Tomographic map of 3D data with a dimension described by probability distribution

I have a three dimensional data set. Two first components are the exact values of(X,Y) and for the third dimension I have a probability attached to each point for each given value of z between (0,1.5). for example P(x0,y0,z0)=0.24 and the probability is not necessarily Gaussian, it can be...
18. ### Help with Probabilistic Modeling with many elements in simulation with unknown probs.

I'm wanting to create a probabilistic model based on several simulations, where I have a binary outcome (go or no-go) and a variable input. The old way of formulating the proability distribution was a straight-forward, curve-fitting of the input variable versus the "go or no-go" outcomes...
19. ### Finding the probability distribution of a dataset

Hello, I have a dataset of 100 numbers. The numbers seem to be random. I wanna find the probability distribution of the dataset. How can I do it mathematically? I would really appreciate a reply. Thank you Sujeeth Kumaravel
20. ### Proof the sum of two CDF's is a CDF.

This is a question my instructor asked in the last midterm exam but nobody was able to solve and he's suggesting it may come out again in the finals: If F(x) and G(X) are two CDF's, prove that H(X) is also a CDF if H(X) = F(X)+G(X)-F(x)G(X) He said something about right...