Cdf of continous RV transformation

In summary, the CDF (cumulative distribution function) of a continuous random variable transformation is a mathematical function that defines the probability that a continuous random variable will take on a value less than or equal to a given value. It is calculated by integrating the probability density function (PDF) of the transformed variable over the range of values from negative infinity to the given value. This integration gives the area under the PDF curve up to that specific value. The CDF of a continuous random variable transformation is an important tool in statistics as it allows for the calculation of probabilities for specific values or ranges of values of the transformed variable. Changing the transformation of a continuous random variable can significantly alter its CDF, as different transformations can result in different probability distributions.
  • #1
Laura1321412
24
0

Homework Statement



Let f(x)= 2x , 0<x<1 , zero elsewhere, be the pdf of X.
Compute the cdf of Y=1/X

Homework Equations



cdf of X = p(X< x)




The Attempt at a Solution



P(1/X <= y)
= P(X <= 1/y)
int 2x from 0 to 1/y
= x^2 eval from 0 to 1/y
= 1/y^2

so the cdf is 1/y^2 for 1<y<infinty

however i don't think this is right... the textbook answers state the cdf as 1-1/y^2


so I am confused. thanks for any help!
 
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  • #2
Since 2 < 4, does this imply that 1/2 < 1/4?

RGV
 

FAQ: Cdf of continous RV transformation

1. What is a CDF of continuous RV transformation?

The CDF (cumulative distribution function) of a continuous random variable transformation is a mathematical function that defines the probability that a continuous random variable will take on a value less than or equal to a given value. It is used to describe the probability distribution of a transformed continuous random variable.

2. How is the CDF of continuous RV transformation calculated?

The CDF of a continuous random variable transformation is calculated by integrating the probability density function (PDF) of the transformed variable over the range of values from negative infinity to the given value. This integration gives the area under the PDF curve up to that specific value.

3. What is the role of the CDF of continuous RV transformation in statistics?

The CDF of a continuous random variable transformation is an important tool in statistics as it allows for the calculation of probabilities for specific values or ranges of values of the transformed variable. It also helps in determining the mean, variance, and other descriptive statistics of the transformed variable.

4. How does changing the transformation of a continuous random variable affect its CDF?

Changing the transformation of a continuous random variable can significantly alter its CDF. This is because different transformations can result in different probability distributions, which in turn, affect the shape and properties of the CDF.

5. Can the CDF of a continuous RV transformation be used to find the probability of a specific outcome?

Yes, the CDF of a continuous random variable transformation can be used to find the probability of a specific outcome by plugging in the desired value into the CDF function. This will give the probability that the transformed variable will take on a value less than or equal to the given value.

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