Chapter 4: Problem 4
Compute an approximate probability that the mean of a random sample of size 15
from a distribution having pdf \(f(x)=3 x^{2}, 0
Chapter 4: Problem 4
Compute an approximate probability that the mean of a random sample of size 15
from a distribution having pdf \(f(x)=3 x^{2}, 0
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Get started for freeLet \(Y_{1}\) denote the minimum of a random sample of size \(n\) from a
distribution that has pdf \(f(x)=e^{-(x-\theta)}, \theta
Let \(X_{1}, X_{2}, \ldots, X_{n}\) be a random sample of size \(n\) from a distribution that is \(N\left(\mu, \sigma^{2}\right)\), where \(\sigma^{2}>0 .\) Show that the sum \(Z_{n}=\sum_{1}^{n} X_{i}\) does not have a limiting distribution.
Let \(\left\\{a_{n}\right\\}\) be a sequence of real numbers. Hence, we can also say that \(\left\\{a_{n}\right\\}\) is a sequence of constant (degenerate) random variables. Let \(a\) be a real number. Show that \(a_{n} \rightarrow a\) is equivalent to \(a_{n} \stackrel{P}{\rightarrow} a\)
Let \(X_{1}\) and \(X_{2}\) have a trinomial distribution with parameters \(n, p_{1}, p_{2}\). (a) What is the distribution of \(Y=X_{1}+X_{2} ?\) (b) From the equality \(\sigma_{Y}^{2}=\sigma_{1}^{2}+\sigma_{2}^{2}+2 \rho \sigma_{1} \sigma_{2}\), once again determine the correlation coefficient \(\rho\) of \(X_{1}\) and \(X_{2}\)
Let \(X_{1}, X_{2}, X_{3}, X_{4}\) be four iid random variables having the same
pdf \(f(x)=\) \(2 x, 0
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