Question

Let X be given by its distribution function F(x) , such that f(x) = 0 if x<=0 f(x) = 1/16 x^4, if 0 < x <=2 f(x) = 1 , if x > 2. Graph the density function. Graph the distribution function F(x). I have already found E(x), Var(x), and SD(x) for this problem, but am not sure how to graph it.

Answer 1

seems to be a piecewise function ....

Answer 2

f(x) = 0 if x<=0
= 1/16 x^4, if 0 < x <=2
= 1 , if x > 2

you do realise that this is not a probability distribution right? the area under the grap is not equal to 1 is it?

Answer 3

should be something akin to that

Answer 4

I just realized I typed the question in not quite right. Sorry about that. It is F(X)=0 if x is less than or equal to 0. F(X)= x^2 divided by 4 if 0 is less than x which is less than or equal to 2. F(X)= 1 if x is greater than 2.

Answer 5

Like I said the teacher wanted me to draw a graph the distribution function and the density function and find E(X), Var(X), and SD(X). I tried finding examples in our notes that fit this problem with no luck. What I am wondering is if I am supposed to plug in the E(X), Var(X), and SD(X) to graph it or just do it purely based on the information given in the question. I am not quite sure where to even begin really.

Answer 6

the distribution function is just the graph of the function .... for example, the distribution function for the normal distribution is the graph of e^(-x^2/2)/sqrt(2pi); which gets us the usual looking bell curve.