Chapter 9: Problem 474
Arrange the values \(7,8,5,10,3\) in ascending order and identify the value of the median.
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Suppose that flaws in plywood occur at random with an average of one flaw per 50 square feet. What is the probability that a 4 foot \(\times 8\) foot sheet will have no flaws? At most one flaw? To get a solution assume that the number of flaws per unit area is Poisson distributed.
A new treatment plan for schizophrenia has been tried for 6 months with 54 randomly chosen patients. At the end of this time, 25 patients are recommended for release from the hospital; the usual proportion released in 6 months is \((1 / 3)\). Using the normal approximation to the binomial distribution, determine whether the new treatment plan has resulted in significantly more releases than the previous plan. Use a \(0.05\) level of significance.
Let Y be distributed with a Pareto distribution with parameters \(\mathrm{X}_{0}\) and \(\theta .\) The density function of such a random variable is: $$ \begin{aligned} \mathrm{f}(\mathrm{y})=\left(\theta \mathrm{X}_{0}^{\theta}\right) /\left(\mathrm{y}^{\theta+1}\right) & \mathrm{y}>\mathrm{X}_{0} \\ \text { with } \mathrm{X}_{0}, \theta>0 \end{aligned} $$ otherwise. What is the variance of \(\mathrm{Y}\) ?
Find \(\mathrm{E}(\mathrm{X})\) for the continuous random variables with
probability density functions;
a) \(f(x)=2 x, 0
\(\mathrm{X}\) is a discrete random variable with probability mass function, \(\mathrm{f}(\mathrm{x})=1 / \mathrm{n}, \mathrm{x}=1,2,3, \ldots, \mathrm{n} ;=0\) otherwise. If \(\mathrm{Y}=\mathrm{X}^{2}\), find the probability mass function of \(\mathrm{Y}\).
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