Let x1,...,x,, be an independent trials process where each X; has the following distribution: P(X₁ = 1) = p, and P(X = 0) = 1 p. Let us find out how many trials are needed to get 68% confidence intervals (d = 1) for the actual mean with lengths less than 0.431. What is E(X)? What is V(X)? (your answer should be a formula with p) (your answer should be a formula with p) Let us find a bound on V(X;) using calculus (the first derivative test). Let f(p) be a function whose formula is your answer to what V(X;) is. The function f(p) has a critical point at p = (give an exact answer) so the maximum value (absolute maximum or global maximum) of f(p) = V(X;) is (give an exact answer) In other words, V(X;) is less than or equal to your answer here, which in turn means ✓V(✗;) is less than or equal to (give an exact answer) Using this information, how many trials n are needed so that the 68% confidence interval for the actual mean has a length that is less than 0.431? (round up to the next highest integer)
Let x1,...,x,, be an independent trials process where each X; has the following distribution: P(X₁ = 1) = p, and P(X = 0) = 1 p. Let us find out how many trials are needed to get 68% confidence intervals (d = 1) for the actual mean with lengths less than 0.431. What is E(X)? What is V(X)? (your answer should be a formula with p) (your answer should be a formula with p) Let us find a bound on V(X;) using calculus (the first derivative test). Let f(p) be a function whose formula is your answer to what V(X;) is. The function f(p) has a critical point at p = (give an exact answer) so the maximum value (absolute maximum or global maximum) of f(p) = V(X;) is (give an exact answer) In other words, V(X;) is less than or equal to your answer here, which in turn means ✓V(✗;) is less than or equal to (give an exact answer) Using this information, how many trials n are needed so that the 68% confidence interval for the actual mean has a length that is less than 0.431? (round up to the next highest integer)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Let x1,...,x,, be an independent trials process where each X; has the following distribution:
P(X₁
= 1) = p, and P(X = 0) = 1 p.
Let us find out how many trials are needed to get 68% confidence intervals (d = 1) for the actual mean with lengths less than 0.431.
What is E(X)?
What is V(X)?
(your answer should be a formula with p)
(your answer should be a formula with p)
Let us find a bound on V(X;) using calculus (the first derivative test). Let f(p) be a function whose formula is your answer to what V(X;) is.
The function f(p) has a critical point at p =
(give an exact answer)
so the maximum value (absolute maximum or global maximum) of f(p) = V(X;) is
(give an exact answer)
In other words, V(X;) is less than or equal to your answer here, which in turn means ✓V(✗;) is less than or equal to
(give an exact answer)
Using this information, how many trials n are needed so that the 68% confidence interval for the actual mean has a length that is less than 0.431?
(round up to the next highest integer)
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