I think you mean that we selected X from a uniform distribution on the intervald (-1,2).jeka131404 said:We selected X point from interval (-1,2).
If X=x, we selected point Y from (-1,x^2).
Define the function of density of the random variable Y.
The density function of a random variable is a mathematical function that describes the distribution of the values that the random variable can take. It specifies the probability of the random variable taking on a particular value or falling within a certain range of values.
The density function and the probability function are both used to describe the distribution of a random variable. However, the density function is used for continuous random variables, while the probability function is used for discrete random variables.
The cumulative distribution function (CDF) is the integral of the density function and represents the probability that the random variable is less than or equal to a specific value. In other words, the CDF is the area under the density function curve.
The density function is used to calculate the probability of a random variable falling within a certain range of values. This is useful in statistical analysis for determining the likelihood of certain events occurring or for making predictions based on the distribution of the data.
Yes, the expected value of a random variable can be calculated from the density function. The expected value is the mean of the random variable and can be found by taking the integral of the product of the random variable and its density function over all possible values.