1. T

    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. F

    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. S

    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. Z

    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. Z

    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. ChristinaScience

    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?) I’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. ChristinaScience

    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. B

    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(λhat) = ?? Given that I've already done the working to show that the MLE of λ is equal to xbar (the sample mean). Any help is much appreciated :rolleyes:
  9. J

    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. S

    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. S

    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. J

    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. N

    (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. J

    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. J

    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. J

    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. F

    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. S

    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. J

    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. J

    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...