Chapter 3: Problem 11
Let \(X\) have a Poisson distribution. If \(P(X=1)=P(X=3)\), find the mode of the distribution.
Chapter 3: Problem 11
Let \(X\) have a Poisson distribution. If \(P(X=1)=P(X=3)\), find the mode of the distribution.
All the tools & learning materials you need for study success - in one app.
Get started for free. Let the random variable \(X\) be \(N\left(\mu, \sigma^{2}\right) .\) What would this distribution be if \(\sigma^{2}=0 ?\) Hint: Look at the mgf of \(X\) for \(\sigma^{2}>0\) and investigate its limit as \(\sigma^{2} \rightarrow 0\).
For the Burr distribution, show that $$ E\left(X^{k}\right)=\frac{1}{\beta^{k / \tau}} \Gamma\left(\alpha-\frac{k}{\tau}\right) \Gamma\left(\frac{k}{\tau}+1\right) / \Gamma(\alpha) $$ provided \(k<\alpha \tau\)
Let \(X_{1}\) and \(X_{2}\) be independent random variables. Let \(X_{1}\) and
\(Y=X_{1}+X_{2}\) have chi-square distributions with \(r_{1}\) and \(r\) degrees of
freedom, respectively. Here \(r_{1}
If \(X\) is \(\chi^{2}(5)\), determine the constants \(c\) and \(d\) so that
\(P(c
Show that $$ Y=\frac{1}{1+\left(r_{1} / r_{2}\right) W} $$ where \(W\) has an \(F\) -distribution with parameters \(r_{1}\) and \(r_{2}\), has a beta distribution.
What do you think about this solution?
We value your feedback to improve our textbook solutions.