Question

We can work with factorial moments to calculate the moments of discrete distributions. a.) Calculate the...

We can work with factorial moments to calculate the moments of discrete distributions.

a.) Calculate the factorial moment of E(X(X-1)) for the binomial and poisson distributions. Then use the results to find the variances of the binomial and poisson distributions.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
: The Root Mean Square of a discrete-time signal is given by We can easily calculate...
: The Root Mean Square of a discrete-time signal is given by We can easily calculate the RMS of signals in MATLAB using a combination of the sum, sqrt, and ^ commands. N represents the number of samples of the signal. Please note that the command .^ applied to a vector squares each element of the vector. Write a script to calculate the RMS of the discrete-time signal x, defined as follows: n = a vector of number between -23...
Problem 3 (m.g.f. of Binomial random variables). We proved that the m.g.f. ψX(t) “generates” the moments...
Problem 3 (m.g.f. of Binomial random variables). We proved that the m.g.f. ψX(t) “generates” the moments of the random variable X by differentiation, and computation at t = 0 (rather than by integration or summation, which is typically harder). For example, ψ 0 X(0) = E(X), ψ00 X(0) = E(X 2 ), . . . , ψ(n) X (0) = E(X n ), where the superscript (n) indicates the n th derivative. (a) Assume that X ∼ Binomial(n, p), i.e....
Problem 1: Relations among Useful Discrete Probability Distributions. A Bernoulli experiment consists of only one trial...
Problem 1: Relations among Useful Discrete Probability Distributions. A Bernoulli experiment consists of only one trial with two outcomes (success/failure) with probability of success p. The Bernoulli distribution is P (X = k) = pkq1-k, k=0,1 The sum of n independent Bernoulli trials forms a binomial experiment with parameters n and p. The binomial probability distribution provides a simple, easy-to-compute approximation with reasonable accuracy to hypergeometric distribution with parameters N, M and n when n/N is less than or equal...
You must decide which of two discrete distributions a random variable X has. We will call...
You must decide which of two discrete distributions a random variable X has. We will call the distributions p0 and p1. Here are the probabilities they assign to the values x of X: x 0 1 2 3 4 5 6 p0 0.1 0.1 0.2 0.3 0.1 0.1 0.1 p1 0.1 0.3 0.2 0.1 0.1 0.1 0.1 You have a single observation on X and wish to test H0: p0 is correct Ha: p1 is correct One possible decision procedure...
The range of a discrete random variable X is {−1, 0, 1}. Let MX (t) be...
The range of a discrete random variable X is {−1, 0, 1}. Let MX (t) be the moment generating function of X, and let MX(1) = MX(2) = 0.5. Find the third moment of X, E(X^3).
The range of a discrete random variable X is {−1, 0, 1}. Let MX(t) be the...
The range of a discrete random variable X is {−1, 0, 1}. Let MX(t) be the moment generating function of X, and let MX(1) = MX(2) = 0.5. Find the third moment of X, E(X^3 )
QUESTION 1 The expected value of a discrete random variable is: A)The mean B)The standard deviation...
QUESTION 1 The expected value of a discrete random variable is: A)The mean B)The standard deviation C) The probability of success D) The variance QUESTION 2 Expected value is: A)A measure of dispersion B) A measure of central location C)A measure of distance from the mean D)None of the above QUESTION 3 In combinations, A)n represents the number of objects, x represents multiply B)n represents nothing, x represents the number of elements C)n represents the total number of objects, x...
(i) If a discrete random variable X has a moment generating function MX(t) = (1/2+(e^-t+e^t)/4)^2, all...
(i) If a discrete random variable X has a moment generating function MX(t) = (1/2+(e^-t+e^t)/4)^2, all t Find the probability mass function of X. (ii) Let X and Y be two independent continuous random variables with moment generating functions MX(t)=1/sqrt(1-t) and MY(t)=1/(1-t)^3/2, t<1 Calculate E(X+Y)^2
Consider a discrete random variable X with probability mass function P(X = x) = p(x) =...
Consider a discrete random variable X with probability mass function P(X = x) = p(x) = C/3^x, x = 2, 3, 4, . . . a. Find the value of C. b. Find the moment generating function MX(t). c. Use your answer from a. to find the mean E[X]. d. If Y = 3X + 5, find the moment generating function MY (t).
Method of Moments Concept Question II 1 point possible (graded) Let (E,{Pθ}θ∈Θ) denote a statistical model...
Method of Moments Concept Question II 1 point possible (graded) Let (E,{Pθ}θ∈Θ) denote a statistical model associated to a statistical experiment X1,…,Xn∼iidPθ∗ where θ∗∈Θ is the true parameter. Assume that Θ⊂Rd for some d≥1. Let mk(θ):=E[Xk] where X∼Pθ. mk(θ) is referred to as the k-th moment of Pθ . Also define the moments map: ψ:Θ →Rd θ ↦(m1(θ),m2(θ),…,md(θ)). What conditions on ψ do we have to assume so that the method of moments produces a consistent and asymptotically normal estimator?...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT