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

In summary, a cumulative distribution function, or CDF, is a mathematical function that shows the probability of a random variable being less than or equal to a specific value. It is calculated by taking the sum of all probabilities of the variable being less than or equal to a given value. The CDF differs from a probability distribution function (PDF) in that it provides the probability of the variable taking on a specific value, while the PDF gives the probability of the variable being within a certain range. The CDF can be used to find the probability of a specific event occurring by subtracting the CDF at the lower bound from the CDF at the upper bound. It can also be used to find the median of a set of data, which
  • #1
tiffyuyu
2
0
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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  • #2
There are characters in your post that need to be edited, and can you show what you have done so far so our helpers see where you are stuck?
 

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

1. What is a cumulative distribution function (CDF)?

A cumulative distribution function, or CDF, is a mathematical function that shows the probability of a random variable being less than or equal to a specific value. It is often used to describe the overall distribution of a set of data.

2. How is the CDF of a random variable X calculated?

The CDF of a random variable X is calculated by taking the sum of all probabilities of X being less than or equal to a given value. This can be represented by the equation F(x) = P(X ≤ x), where F(x) is the CDF of X and P(X ≤ x) is the probability of X being less than or equal to x.

3. What is the difference between a CDF and a probability distribution function (PDF)?

The CDF and PDF are both used to describe the distribution of a set of data, but they differ in the information they provide. The CDF gives the probability of a random variable being less than or equal to a specific value, while the PDF gives the probability of the random variable taking on a specific value.

4. How can a CDF be used to find the probability of a specific event occurring?

The CDF can be used to find the probability of a specific event occurring by subtracting the CDF at the lower bound from the CDF at the upper bound. This can be represented by the equation P(a < X ≤ b) = F(b) - F(a), where P(a < X ≤ b) is the probability of X being between a and b, and F(a) and F(b) are the CDFs at a and b, respectively.

5. Can the CDF be used to find the median of a set of data?

Yes, the median of a set of data can be found using the CDF. The median is the value at which the CDF is equal to 0.5. This means that 50% of the data falls below the median and 50% falls above it.

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