Question

(18) Show that the mode of a beta(a,b) random variable is (a−1)/(a+b−2) when a > 1...

(18) Show that the mode of a beta(a,b) random variable is
(a−1)/(a+b−2) when a > 1 and a + b > 2.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let X ~ beta(alpha, beta). Find the population mode of X for alpha > 1 and...
Let X ~ beta(alpha, beta). Find the population mode of X for alpha > 1 and beta > 1.
1. Show that the median of continuous random variable with positive p.d.f. is uniquely defined. 2....
1. Show that the median of continuous random variable with positive p.d.f. is uniquely defined. 2. Exhibit an example of a continuous random variable for which the median is not uniquely defined.
How to show a random variable is not an uniform variable? In particular, please show that:...
How to show a random variable is not an uniform variable? In particular, please show that: X1 is uniform in [0, 1], X2 is uniform in [1, 2], but X1+ X2 is not uniform variable.
A random variable X with a beta distribution takes on values between 0 and 1, with...
A random variable X with a beta distribution takes on values between 0 and 1, with unknown α and β. a) Use the method of moments to obtain an estimator forαandβ. b) Are the estimators sufficient statistics?
1. Show that if X is a Poisson random variable with parameter λ, then its variance...
1. Show that if X is a Poisson random variable with parameter λ, then its variance is λ 2.Show that if X is a Binomial random variable with parameters n and p, then the its variance is npq.
Let U be a random variable that is uniformly distributed on (0; 1), show how to...
Let U be a random variable that is uniformly distributed on (0; 1), show how to use U to generate the following random variables: (a) Bernoulli random variable with parameter p; (b) Binomial random variable with parameter n and p; (c) Geometric random variable with parameter p.
A Poisson random variable is a variable X that takes on the integer values 0 ,...
A Poisson random variable is a variable X that takes on the integer values 0 , 1 , 2 , … with a probability mass function given by p ( i ) = P { X = i } = e − λ λ i i ! for i = 0 , 1 , 2 … , where the parameter λ > 0 . A)Show that ∑ i p ( i ) = 1. B) Show that the Poisson random...
Consider a random variable X such that: ??(?) =|?| / 2? ??? ? ∈ {−2, −1,...
Consider a random variable X such that: ??(?) =|?| / 2? ??? ? ∈ {−2, −1, 1, 2}, ??(?) = 0 ??? ? ∉ {−2, −1, 1, 2}, Where ? > 0 is a real parameter. a) Find a. b) What is the PMF of the random variable ? =?^2+1/?? Guidance: ? is a function of ? (? = ?(?)). Write P(? = ?) in terms of P(? = ?) such that ? = ?(?). You can make use of...
If X is a continuous random variable with pdf f(x) on the interval [a,b] then show...
If X is a continuous random variable with pdf f(x) on the interval [a,b] then show that a<E(X)<b.
Give the definition of memoryless for a random variable X. (b) Show that if X is...
Give the definition of memoryless for a random variable X. (b) Show that if X is an exponential random variable with parameter λ, then X is memoryless. (c) The life of the brakes on a car is exponentially distributed with mean 50,000 miles. What is that probability that a car gets at least 70,000 miles from a set of brakes if it already has 50,000 miles?