Statistics homework help!!!!!!!!!!?

Question

The following is a continuous random variable: Start at (0,.3) to (1,.3) to (1.5,.5) to (2,.3) to (3,.3)

Find the following probabilities:
i. P(X>1)
ii. P(X<1)
iii. P(X=1)
iv. P(.5 v. P(.5
Now I'm not just someone looking for the answers, I actually want to figure out how to work them. They keep telling me to use the area formula, but I still can't figure out the length and width. If someone could please help, I would greatly appreciate it.

Answer 1

I am making the assumpition that the points you are given form the probability density distribution curve p(x) for the random variable. This means that P(a
Start by plotting the distribution from the points given. The probability of a point being within a range is the area under the curve within that range . Use geometry to compute these areas: break up the figure into rectangles and triangles. First get the full area, call that A (this should come out 1). The width of the area you want is the limit of the values given; in case i, that would be the distance from x = 1 to the right-hand limit of the curve at x = 3, or ∆x = 2.

To show you how, here is the way to get the full curve area A:

Rectangle from (0,.3 to (3,.3): Base 3 height .3, area .9
Triangle from (1,.3) to (1.5,.5) to (2,.3): Base 1, altitude (.5-.3) = .2, area = .5*1*.2 = .1

Total area = 1 (as it should).

Area for P(x>1) rectangle base 2, height .3, area .6; triangle base 1 altitude .2, area .1, then P(x>1) = .7, the sum of the areas.

From a probabiliy distribution, you cannot get the probability of a single value, only a range.

You will have to interpolate altitudes for points that do not coincide with the ones given.

EDIT: I have made a drawing of the distribution if that will help. Find it at http://img218.imageshack.us/img218/8930/distributionhg6.png