# distribution

1. ### card distribution question

Hello everyone. This is my first post here and allow me to first say I am not a big expert on statistics so it's help what I am looking for here :) Here the problem: I have 15 cards and 5 players. Each player receives 3 cards, and for me it's not important in which order. In how many...
2. ### Generate a random number folowing a given distribution

Hello, I have a question, Im not sure if there even exists a solution. I read that one can generate normally distributed random values from uniformly distributed ones. Is there a way of generating a random number, folowing a given distribution, out of a limited count of given uniformly...
3. ### Branching process of Poisson distribution

I am having some problems with this problem: Consider a branching process in which the family size distribution is Poisson with mean $\lambda$. (a) Under what condition will the probability of extinction of the process be less than 1? (b) Find the extinction probability when...
4. ### joint probability distribution.

Let X be a random variable with values 0, 1 and 3, and let Y be a random variable with values -1, 1, 2, with the following joint distribution: Y -1 1 2 ---------------------- 0 | 0.12 0.08 0.10 X 1 | 0.20 0.04 0.25 3 | 0.08 0.10 0.03...
5. ### joint probability distribution.

How do you construct a joint probability distribution over E, F, and G such that P(E) = 1/2, P(E|F) = 3/4, P(E|G) = 4/5 but P(E|F,G) = 1/10?? Any hints or idea would be much appreciated. Thanks.
6. ### Skewed Distribution

I need help with the skewness. If you can so kindly explain and show an example of how they are skewed (e.g., negatively or positively skewed?) Iâ€™m so lost for this part. I read the book, but the book only gives a definition - no examples or demonstrations. Here is what I know about...
7. ### Frequency Distribution

Hello, :) I completed a practice assignment, but I am not sure if I did this right or incorrectly. I haven't received the textbook yet, but it's on the way. Can you check to see if I am doing this correctly/incorrectly? If I made a mistake, can you please explain step-by-step in very simple...
8. ### Estimator for Poisson Distribution

Hi!! New here, my first post. Looking for some help on how to find the Variance of the Maximum Likelihood Estimator, that is Var(Î»hat) = ?? Given that I've already done the working to show that the MLE of Î» is equal to xbar (the sample mean). Any help is much appreciated :rolleyes:
9. ### Distribution - Fourier series

Good day, I am trying to solve an exercise in the course of distribution theory and fourier analysis. I am new to the matter of using distribution in calculating, and I am thankful for any help to solve the following question: 1. Consider the $2\pi$ -periodic function $f(x)$ defined on...
10. ### The P.M.F. of Hypergeometric and Negative Binomial Distribution.

A forest contains 100 deer. 20 of them have a red tag and 80 of them are untagged. A researcher samples 30 random deer without replacement. Let X be the number of tagged deer in the sample. From the sample of 30 deer, she will keep picking deer with replacement until she picks the fourth tagged...
11. ### Poisson distribution problem.

For a shirt ironing service at the dry cleaners, they charge a base price of \$3 plus an additional \$1.50 per shirt to be ironed. Suppose the number of shirts customers at the dry cleaners require to be ironed follows a Poisson distribution with mean 4.5. What is the probability a random...
12. ### Posterior Distribution from Beta Density with Exponential Prior

Let $X_1,...,X_n$ be iid random variables with a common density function given by: $f(x|\theta)=\theta x^{\theta-1}$ for $x\in[0,1]$ and $\theta>0$. Put a prior distribution on $\theta$ which is $EXP(2)$, where $2$ is the mean of the exponential distribution. Obtain the posterior...
13. ### (normal distribution) E(e^x) and median of e^x of N(2,5)

Dear all, Started with a statistics course and even the basic concepts are a problem for me. Reason for that is that there are no examples in the book and just a bunch of formulas. It makes it hard to grasp the concept. I hope one can help me out! So the question is: IF x ~ N(2,5) what is...
14. ### Burr Distribution Derivation from Inverse Weibull

A Weibull distribution, with shape parameter alpha and Am I supposed to find the MGFs of both distributions and then use the iterated rule/smoothing technique/law of total expectation followed by uniqueness theorem to find the PDF of the Burr distribution? Or am I supposed to use the...
15. ### Joint Moment Generating Function from Conditional and Marginal Distribution

Suppose that that random variable $N$ follows a Poisson distribution with mean $\lambda=6$. Suppose that the conditional distribution of the random variable $X$, given that $N=n$, follows that of a $Binomial(n,0.6)$. Find the Joint Moment Generating Function of $(N, X)$. Initially I just...
16. ### Sampling Distribution of Normal Random Variables

Let $X_1,X_2,...,X_m$ be i.i.d. from a $N(\mu_1,\sigma_1^2)$ distribution, and let $Y_1,Y_2,...,Y_n$ be i.i.d. from a $N(\mu_2,\sigma_2^2)$ distribution, and let the $X_i$'s be independent from the $Y_j$'s. Determine the sampling distribution of the following quantity...
17. ### How to calculate the expectation of a joint probability distribution com

a strange joint probability problem For example, F (x, y) is a two-dimensional joint probability distribution function, where X is a normal normal distribution, Y is 0-1 binomial distribution with parameter q. How to find the expectation of F (x, y)? thanks for solving this problem
18. ### Two random variables equal in distribution

Hi ! Can we find two random variables that are equal in distribution but are not equal ? Thanks in advance ! :)
19. ### Interpretation of Limiting Distribution

Let $X_1, ..., X_n$ be random variables independent and identically distributed on $Uniform(0,1)$. Let $X_{(n)}=MAX{(X_1,...,X_2)}$. Define $W_n=n(1-X_{(n)})$. Find the limiting distribution of $W_n$ as $n$ increases without bound. Can you identify this limiting distribution? Give an...
20. ### Distribution of a Monotonic Function of a Discrete Random Variable

Suppose I have a discrete random variable $Y$ with PMF $f(y)$ and support $\lbrace 1, 2, ..., N \rbrace$. Suppose I define another discrete random variable $H=Floor(Log_2(Y))$. Floor is simply the function which returns the integer part of a value, so all decimal points are truncated...