Question

probability & stats help, anyone ?

Answer 1

Can you post a question?

Answer 2

Let f(x) be the PDF of a random variable X defined as
Ax^2 when 0<x<1; A when 1<x<2; and 0 elsewhere.

a) Determine the constant A.
b) Find CDF of X
c) Find the chance that X is less than 1.5.
d) Find the probability that X is between 0.5 and 3.
e) Find the mean and variance of X.

Answer 3

It appears that the probability density function of the random variable X has the domain (0, 2). In other words, this function is zero on (-infinity, 0] and again zero on [2, +infinity).

Recall that the total area of a prob. density function is always 1 (one).

Just for example, suppose that the probability density function had the same value for all x in its domain. What would the height of the rectangular area boxed in by x=0, x=2, y=0 and y=b be? Hint: how do you find the area of a rectangle, given the length and height?

Answer 4

for finding the constant

Answer 5

is that right ?

Answer 6

The Probability Density Function (PDF) is given by Ax^2 when 0<x<1; A when 1<x<2.

Can you draw the two different graphs that define the upper boundary of the PDF?
You could:

1. Simply assume that A=1 and graph the upper boundary accordingly. The first half of this curve would be part of a parabola; the 2nd half would be a horiz. straight line.
2. Calculate the area under this upper boundary, between 0 and 2. It will be more than 1, and therefore wrong.
3. Figure out what smaller value A must take on so that the area under the upper boundary will be exactly 1.

Answer 7

Draw: Ax^2 when 0<x<1; A when 1<x<2, first assuming that A=1 (which is false).