sneaky666 said:X1,X2,...,Xn is a sample from a distribution with cdf F. Show
FX(i)(x)= [tex]\sum[/tex][tex]\stackrel{n}{j=i}[/tex] ([tex]\stackrel{n}{j}[/tex]) Fj(x)(1-F(x))(n-j)
How would I start on this?
A cdf, or cumulative distribution function, is a statistical function that shows the probability of a random variable being less than or equal to a certain value. In other words, it maps out the cumulative probability distribution of a random variable.
A pdf, or probability density function, gives the probability of a random variable falling within a certain range of values. A cdf, on the other hand, gives the probability of the random variable being less than or equal to a certain value. In other words, a cdf is the integral of the pdf.
To calculate the cdf, you need to integrate the pdf function over the desired range of values. It is also possible to use a table or graph to estimate the cdf. In some cases, the cdf may have a closed-form expression that can be calculated directly.
The cdf is useful in determining the likelihood of a certain outcome in a probability distribution. It can also be used to calculate percentiles, which are useful in understanding the spread of data and making comparisons between different datasets.
Yes, a cdf can be used for any probability distribution, including non-parametric distributions. In these cases, the cdf is typically estimated using techniques such as the empirical cdf, which uses the actual data points to estimate the cdf.