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Two numbers are selected at random from the interval (0, 1). If these values are uniformly and independently distributed, by cutting the interval at these numbers, compute the probability that the three resulting line segments can form a triangle.

Let be the order statistics of a random sample of size n from the exponential distribution with pdf zero elsewhere.

Let  be a random sample from a distribution of either type. A measure of spread is Gini’s mean difference

In the Program Evaluation and Review Technique (PERT), we are interested in the total time to complete a project that is comprised of a large number of subprojects. For illustration, let  be three independent random times for three subprojects. If these subprojects are in series (the first one must be completed before the second starts, etc.),

1. Let Yn denote the nth order statistic of a random sample of size n from a distribution of the continuous type. Find the smallest value of n for which the inequality 2. Let denote the order statistics of a random sample of size 5 from a distribution of the continuous type. Compute:

Compute are the order statistics of a random sample of size 9 from a distribution of the continuous type. Find the smallest value of n for whichare the order statistics of a random sample of size n from a distribution of the continuous type.

Verzani (2014), page 323, presented a data set concerning the effect that different dosages of the drug AZT have on patients with HIV. The responses we consider are the p24 antigen levels of HIV patients after their treatment with AZT. Of the 20 HIV patients in the study, 10 were randomly assign the dosage of

Verzani (2014), page 323, presented a data set concerning the effect that different dosages of the drug AZT have on patients with HIV. The responses we consider are the p24 antigen levels of HIV patients after their treatment with AZT. Of the 20 HIV patients in the study, 10 were randomly assign the dosage of

In Exercise 4.2.18 we found a confidence interval for the variance σ2 using  Exercise 4.2.18 Let  be a random sample from N(μ, σ2), where both param  (a) Show that this second probability statement can be written as (b) If n = 9 and s2 = 7.93, find a 95% confidence interval for σ2. (c) If μ is known,

Let p equal the proportion of drivers who use a seat belt in a country that does not have a mandatory seat belt law. It was claimed that p = 0.14. An advertising campaign was conducted to increase this proportion. Two months after the campaign, y = 104 out of a random sample of n