Chapter 3: Problem 9
Determine the 90 th percentile of the distribution, which is \(N(65,25)\).
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Let the mutually independent random variables \(X_{1}, X_{2}\), and \(X_{3}\) be \(N(0,1)\), \(N(2,4)\), and \(N(-1,1)\), respectively. Compute the probability that exactly two of these three variables are less than zero.
Say the correlation coefficient between the heights of husbands and wives is \(0.70\) and the mean male height is 5 feet 10 inches with standard deviation 2 inches, and the mean female height is 5 feet 4 inches with standard deviation \(1 \frac{1}{2}\) inches. Assuming a bivariate normal distribution, what is the best guess of the height of a woman whose husband's height is 6 feet? Find a \(95 \%\) prediction interval for her height.
The mgf of a random variable \(X\) is \(\left(\frac{2}{3}+\frac{1}{3}
e^{t}\right)^{9}\).
(a) Show that
$$
P(\mu-2 \sigma
Let \(X\) and \(Y\) have a bivariate normal distribution with respective
parameters \(\mu_{x}=2.8, \mu_{y}=110, \sigma_{x}^{2}=0.16,
\sigma_{y}^{2}=100\), and \(\rho=0.6 .\) Using \(R\), compute:
(a) \(P(106
Determine the constant \(c\) in each of the following so that each \(f(x)\) is a
\(\beta\) pdf:
(a) \(f(x)=c x(1-x)^{3}, 0
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