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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2010 • Question 6

Question

Math 6010 • Linear Models Spring 2010 • Question 6

Let \(X_1\) and \(X_2\) be independent random variables. The density function function of \(X_1\) is \[ f(t)= \begin {cases} 0, & \text {if } t\notin [0,1],\\ \dfrac {e^t}{e-1}, & \text {if } 0\leq t\leq 1. \end {cases} \] The distribution of \(X_2\) is \[ \mathbb {P}\{X_2=1\}=p \quad \text {and}\quad \mathbb {P}\{X_2=-1\}=q,\qquad p+q=1. \] Compute the moment generating function of \(X_1X_2\).

Raw LaTeX

Let \(X_1\) and \(X_2\) be independent random variables. The density
function function of \(X_1\) is
\[
f(t)=
\begin{cases}
0, & \text{if } t\notin[0,1],\\
\dfrac{e^t}{e-1}, & \text{if } 0\leq t\leq1.
\end{cases}
\]
The distribution of \(X_2\) is
\[
\Prob\{X_2=1\}=p \quad\text{and}\quad \Prob\{X_2=-1\}=q,\qquad p+q=1.
\]
Compute the moment generating function of \(X_1X_2\).

Topic Tags

Covariance and Independence Estimator Distributions Multivariate Normal Distributions Uniform Integrability and Truncation Methods