MHB Please help with this question (cumulative distribution function of X)

AI Thread Summary
The discussion focuses on deriving the cumulative distribution function (CDF) F(x) from the given probability density function (PDF) f(x) = 10/x^2 for x > 10. The participants are tasked with calculating P(X > 20) using the CDF and determining the probability that at least 3 out of 6 devices will last at least 20 hours. Assumptions regarding the independence of device lifetimes are mentioned as crucial for the probability calculations. Additionally, there is a request for clarification on formatting issues in the post, indicating that contributors should provide their progress for better assistance. The thread emphasizes the importance of clear communication and methodical problem-solving in probability theory.
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The probability density function of the lifetime of a certain type of electronic device
(measured in hours), X, is given by

f(x) = 10/x^2,
0,
x > 10;
elsewhere.

(a) Find the cumulative distribution function of X, namely F(x) and hence find
P(X > 20).
(b) What is the probability that of 6 such devices, at least 3 will function for at least 20 hours? What assumption did you make?
 
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