vela said:You're close. Remember that f(x) is non-zero only on the interval [0,1].
vela said:Again: f(x) is non-zero only on the interval [0,1].
vela said:Check your limits of integration, keeping in mind my previous posts.
A change of variable is the process of transforming a random variable into a new random variable. It is important in statistics because it allows for the simplification of complex problems and can make calculations easier. It also allows for the exploration of relationships between variables and can help in making predictions.
To find the cdf of Y, first determine the new variable Y in terms of the original variable X. Then, plug in the values of Y into the cdf formula and solve for the cdf of Y. Make sure to consider any restrictions or bounds on the new variable Y.
Yes, a change of variable can be used for both continuous and discrete random variables. However, the method for finding the cdf of Y may differ slightly for discrete random variables, as it involves summing probabilities instead of integrating.
The cdf of Y provides information about the probability distribution of the new variable Y. It can help in making predictions about the behavior of Y and in calculating probabilities of certain events occurring.
When solving change of variable problems, it is important to carefully consider the relationship between the original and new variables and to clearly define any assumptions or restrictions. It can also be helpful to draw a diagram or sketch to visualize the problem and to check your work by plugging in values for both the original and new variables into the cdf formula.