Math

Let N be a positive integer random variable with PMF of the form

pN(n)=12⋅n⋅2−n,n=1,2,….

Once we see the numerical value of N , we then draw a random variable K whose (conditional) PMF is uniform on the set {1,2,…,2n} .
Write down an expression for the joint PMF pN,K(n,k) .

For n=1,2,… and k=1,2,…,2n :

Find the marginal PMF pK(k) as a function of k .

Let A be the event that K is even. Find P(A|N=n) and P(A) .

P(A∣N=n)=

  1. 👍 1
  2. 👎 0
  3. 👁 1,460
  1. n+1=i have no idea

    1. 👍 0
    2. 👎 0
  2. Anyone?

    1. 👍 0
    2. 👎 0
  3. 3) P(A∣N=n)= 1/(2^n)
    P(A) = 1

    I'm not 100% sure that they are right

    1. 👍 0
    2. 👎 0
  4. Nope all are partially right or entirely wrong..

    1) (1/2)^(n+2)

    2) (1/2)^((k/2)+1)

    3) 1/2 , 1/2

    4) YES

    You are welcome!

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Probability

    Question:A fair coin is flipped independently until the first Heads is observed. Let the random variable K be the number of tosses until the first Heads is observed plus 1. For example, if we see TTTHTH, then K=5. For K=1,2,3...K,

  2. probability

    t the discrete random variable X be uniform on {0,1,2} and let the discrete random variable Y be uniform on {3,4}. Assume that X and Y are independent. Find the PMF of X+Y using convolution. Determine the values of the constants

  3. Probability

    Let Θ1 and Θ2 be some unobserved Bernoulli random variables and let X be an observation. Conditional on X=x, the posterior joint PMF of Θ1 and Θ2 is given by pΘ1,Θ2∣X(θ1,θ2∣x)= 0.26, if θ1=0,θ2=0, 0.26, if

  4. Probability

    Let Θ be an unknown random variable that we wish to estimate. It has a prior distribution with mean 1 and variance 2. Let W be a noise term, another unknown random variable with mean 3 and variance 5. Assume that Θ and W are

  1. probability

    A fair coin is flipped independently until the first Heads is observed. Let K be the number of Tails observed before the first Heads (note that K is a random variable). For k=0,1,2,…,K, let Xk be a continuous random variable

  2. probability

    The random variable X has a PDF of the form fX(x)={1x2,0,for x≥1,otherwise. Let Y=X2 . For y≥1 , the PDF of Y it takes the form fY(y)=ayb . Find the values of a and b . a= b=

  3. Mathematics

    Let Z be a nonnegative random variable that satisfies E[Z4]=4 . Apply the Markov inequality to the random variable Z4 to find the tightest possible (given the available information) upper bound on P(Z≥2) . P(Z≥2)≤

  4. math

    The random variable X is exponential with parameter λ=1 . The random variable Y is defined by Y=g(X)=1/(1+X) . a) The inverse function h , for which h(g(x))=x , is of the form ay^b+c . Find a , b , and c . b) For y∈(0,1] , the

  1. Probability & Statistics

    The random variable X has a standard normal distribution. Find the PDF of the random variable Y , where: 1. Y = 5X−7 . 2. Y = X2−2X . For y≥−1 ,

  2. Probability

    ML estimation Let K be a Poisson random variable with parameter λ: its PMF is pK(k;λ)=λke−λk!,for k=0,1,2,…. What is the ML estimate of λ based on a single observation K=k? (Your answer should be an algebraic function of

  3. Probability

    Let K be a Poisson random variable with parameter λ : its PMF is pK(k;λ)=λke−λk!,for k=0,1,2,…. What is the ML estimate of λ based on a single observation K=k ? (Your answer should be an algebraic function of k using

  4. Probability

    Let Z be a nonnegative random variable that satisfies E[Z^4]=4. Apply the Markov inequality to the random variable Z^4 to find the tightest possible (given the available information) upper bound on P(Z≥2). P(Z>=2)

You can view more similar questions or ask a new question.