Please see the attached file.

Density function of a continous random variable
A continuous random variable X has the following density function:

f(x) = x, 0<=x<=1, = (2-x), 1
f(x) = x, 0 less than and equal to "x" less than and equal to 1, = (2-x), 1 less than x less than or equal to 2.

Full equation on top does not read out on this web site?? See written out problem for clarification.

Note: <= means less than AND equal to

a) Plot the density function
b) Find the median of X
c) Find the variance of X
d) Find P(X=.1 or .2)

Answer

Given that

b).
Median is that value of a for which P(X<a) = 0.5
Thus

Clearly

Thus median = 1

c).
Mean of X = E(X) =

Variance X =

d).
Since the variable X is a continuous random variable P(X=0.1 or 0.2) is Zero