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Given a product X = ITi ∈I Xi of topological spaces (Xi , T ), with product topology, and a directed set J , a net in X indexed by J is given by a doubly indexed family {x ji } j ∈ J,i ∈I . Show that such a net converges for the product topology if and only if for every i ∈ I , the net {x ji } j ∈ J converges in Xi for Ti . (For this reason, the product topology is sometimes called the topology of "pointwise convergence": for each j , we have a function i f→ xij on I , and convergence for the product topology is equivalent to convergence at each "point" i ∈ I . This situation comes up especially when the Xi are [copies of] the same space, such as R with its usual topology. Then ITi Xi is the set of all functions from I into R, often called RI .)
Suppose the true population proportion is 68%. What is the probability of observing a sample proportion 64% or smaller.
suppose xn432. using the standard normal table find the probabilities. 1 p-2.5 less than or equal to x which is less
question a recent study by an automobile dealer revealed the mean amount of profit per car sold for a sample 20
Suppose a sample of 35 surveys shows a sample mean of 17 minutes. Use = 4 minutes. Is the premium rate justified? Formulate the null and alternative hypotheses for this application.
Find the value of x that corresponds to each of these standard scores z = -1.85.
christine has always been weak in mathematics. based on her performance prior to the final exam in calculus there is a
Discuss an example where you would use a test of hypothesis with three or more population means (that can be analyzed using ANOVA technique) at your employment or personal life.
In a study of 24 criminals convicted of antitrust offenses, the average age was 55 years, with a standard deviation of 7.6 years. Construct a 98% confidence interval of the true mean age.
Compute the optimal production quantities for the company?
the degenerative disease osteoarthritis most frequently affects weight-bearing joints such as the knee. the following
Suppose the Doctor would be content with 95% confidence. How does the decrease in confidence affect the sample size required?
A mathematics professor has two umbrellas, both of which were originally at home. The professor walks back and forth between his home and office, and if it is raining when he starts a journey, he carries an umbrella with him unless both his umbrel..
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