You have to do two cases. First take ##-1\le x \le 0## and work that. You will just need one integral. Then take ##x>0## and work that, which will take two integrals with ##x## only in the second one, etc.aquaelmo said:Homework Statement
Consider a continuous random variable X with the probability density function fX(x) = |x|/5 , – 1 ≤ x ≤ 3, zero elsewhere.
I need to find the cumulative distribution function of X, FX (x).
2. Homework Equations
The equation to find the cdf.
The Attempt at a Solution
FX(x) = ∫-1x -u/5 du + ∫-10 -u/5 du + ∫0x u/5 du
For some reason, my result is just a constant, but I can't figure out why my equation is wrong?
No, the second case would be ##\int_{-1}^0 -\frac u 5~ du + \int_0^x \frac u 5 ~du##.aquaelmo said:I believe that's what I'm doing.
For case -1 ≤ x ≤ 0, I compute the integral ∫-1x -u/5 du.
For the case x > 0, I compute the area of the first case, ∫-10 -u/5 du, then the second case, ∫0x u/5 du
A pdf (probability density function) shows the probability of a continuous random variable taking on a specific value, while a cdf (cumulative distribution function) shows the probability of a random variable being less than or equal to a specific value.
To find the cdf given a pdf with absolute value, you can integrate the pdf function from negative infinity to x, where x is the variable. This will give you the cumulative probability up to that point.
A cdf always ranges from 0 to 1, as it represents the cumulative probability of a random variable being less than or equal to a specific value.
No, a cdf must always be a non-decreasing function. This means that it can have any shape as long as it does not decrease at any point.
A cdf is useful in statistics because it allows us to calculate probabilities for continuous random variables, which are often used in real-world situations. It also allows us to determine the median, quartiles, and other important percentiles of a data set.