Learning Materials
Features
Discover
Chapter 4: Q4.2-8E (page 225)
Suppose that a class contains 10 boys and 15 girls, and suppose that eight students are to be selected randomly from the class without replacement. Let X denote the number of boys selected, and let Y denote the number of girls selected. Find E(X 鈭� Y ).
E (X 鈭� Y) = \( - \frac{8}{5}\)
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
IfXhas the uniform distribution on the interval [a, b], write a formula for every even central moment ofX.
Let X have the discrete uniform distribution on the integers \(1, \ldots \ldots ,n\).Compute the variance of X.
Hint: Youmay wish to use the formula \(\sum\limits_{k = 1}^n {{k^2}} = \frac{{n\left( {n + 1} \right)\left( {2n + 1} \right)}}{6}\)
Suppose that X is a random variable for which \(E\left( X \right) = \mu \), and\(Var\left( X \right) = {\sigma ^2}\). Show that\(E\left( {X\left( {X - 1} \right)} \right) = \mu \left( {\mu - 1} \right) + {\sigma ^2}\).
Show that two random variablesXandYcannot possibly have the following properties:\(E\left( X \right) = 3\),\(E\left( Y \right) = 2\),\(E\left( {{X^2}} \right) = 10\),\(E\left( {{Y^2}} \right) = 29\), and\(E\left( {XY} \right) = 0\).
Let X have pdf:
\(f\left( x \right) = \left\{ {\begin{aligned}{{}{}}{{x^{ - 2}};{\rm{ if }}x > 1}\\{0;{\rm{ otherwise}}}\end{aligned}} \right.\)
Prove that the m.g.f.\(\psi \left( t \right)\) is finite for all \(t \le 0\) but for no \(t > 0\).
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine