Use markov-s inequality to prove in probability

Assignment Help Basic Statistics

Reference no: EM13113173

1. Let {Xn : n >=1} be a sequence of positive independent random variables with E(Xn) = c 2 (0; 1) for each n. Let Yn = X1X2...Xn, the product of the Xi's. Use Markov's inequality to prove that Yn ~ 0 in probability.

2. Let X1; : : : ;Xn be iid Unif(0; 1) random variables.

(a) Dene Mn = max(X1; : : : ;Xn). Find the CDF of Mn.
(b) Prove that n(1-Mn) ! Z in distribution, where Z has CDF FZ(z) = 1-e^-z.

Reference no: EM13113173

Questions Cloud

Creating lewis structure for molecules : Draw the Lewis structure for each of the following molecules or ions, and predict their electron-domain and molecular geometries.

Determine the enthalpy change for the dissolution of nh4no3 : how many moles can be produced from 2.5 moles of Ag2CO3 and final temperature of the calorimeter contents is 23.83°C After dissolution of the salt.

Example of two tailed test : Provide an example of a situation from your personal or professional experience where an two-sample test of hypothesis of dependent samples would be useful in a decision-making process.

Application for use of anova : Name an application for the use of ANOVA. This can be in a professional setting, hobby, or something you find on the internet. What are some business situations where ANOVA would be more appropriate than a Z or T test?

Use markov-s inequality to prove in probability : Let {Xn : n >=1} be a sequence of positive independent random variables with E(Xn) = c 2 (0; 1) for each n. Let Yn = X1X2...Xn, the product of the Xi's. Use Markov's inequality to prove that Yn ~ 0 in probability.

Determine the final concentration : Determine the final concentration if A 129 mL portion of that solution is diluted using water of 149 mL.

What is the enthalpy of reaction per mole of oxygen bound : An aqueous solution of unoxygenated hemoglobin containing 5 g of protein (M= 64000 g/mol) in the 100cm3 of solution is placed in an insulated vessel.

Conclude that college students watch fewer videos a month : A random sample of 36 college students revealed that the mean number of videos watched last month was 7.2, with a student deviation of 0.5. At the 0.5 significance level, can we conclude that college students watch fewer videos a month than high s..

Find probability of randomly selecting liberal or male : What is the probability of randomly selecting a person who is conservative and then selecting from that group someone who is a nursing major?

User Account

All Pages