Joint and marginal distribution functions problem

Assignment Help Basic Statistics

Reference no: EM1399310

Let X and Y be continuous random variables.

(i) Show that if X and Y are independent, they they are uncorrelated.

(ii) Prove that X + Y and X - Y are uncorrelated if and only if X and Y have the same variance.

Suppose that the joint probability density function of the continuous random variables U and V is given by

f(u, v) = {6e^(-2u-3v), 0,
u >= 0, v >= 0 otherwise

(iii) Show that U and V are independent.

(iv) Find the probability density function of U + V.

(vi) Let P = 2U + 3V and Q = 2U - 3V. Given that the variances of U and V are 1/4 and 1/9 respectively, show that P and Q are uncorrelated.

Reference no: EM1399310

Questions Cloud

Distribution of household income in the united states : What are the details why this distribution exists? Would it be fair to define the distribution of household income in the United States as unfair? Why or why not? And

Discuss one method to promote diversity within organizations : Discuss one method to promote diversity within organizations. State how implementation of diversity initiatives increase managerial effectiveness.

Estimate the production and productivity : A local market research firm has just won a contract for several thousand small projects involving data gathering and statistical analysis. In the past, the firm has assigned each project to a single member of its highly trained professional staff.

How bioethanol is produced from different land plants : how bioethanol is produced from different land plants.

Joint and marginal distribution functions problem : Find the probability density function of U + V. Let P = 2U + 3V and Q = 2U - 3V. Given that the variances of U and V are 1/4 and 1/9 respectively, show that P and Q are uncorrelated.

Calculate what quantity of potassium chlorate : Calculate what quantity of potassium chlorate that has molecular weight of 122.5 needed to form 33.6 litres of oxygen? Express your answer in grams and assume that temperature and pressue will be in normal condition?

What strategies helpful in sticking to guidelines : When you think the differing types of nutritional needs that people have as grow from infants to senior citizens, write down the most significant general guidelines which must be followed.

Trucks are obligatory to pass through a weighing station : Trucks are obligatory to pass through a weighing station so that they can be checked for weight violations. Trucks reach at the station at the rate of 40 an hour between 7pm and 9pm.

Find advantage and disadvantage of using transgenic bacteria : Discuss the advantages and disadvantages of using transgenic bacteria, yeast and plants in biofuel production.

User Account

All Pages