3 questions for the assignment.

46912 assignment
Conditional Expectation
i) .
a) X is U(0,1)
X is uniform with density function f(x) = 1/(1-0) = 1, 0≤x≤1
To find E(x2)
b) To find cdf of y
c) Using the above to find E(y)
Since cumulative is given by , we have pdf as derivative of this hence =
G(y) = , 0≤y≤1
E(y) =) dy =
Same as above.
ii) Given X any point lying between 0 and 1 divide the interval (0,1) into two parts. Y is U(0.1).
a) If X=x, then we have two subintervals (0,x) and (x,1)
If y is contained that subinterval is selected. Then L is the random variable giving the length of the subinterval
L can be from 0 to 1 excluding 0. i.e. L can take values continuously from 0 to 1.
Y can lie in this interval with prob x and not lie with prob 1-x.
Y lie do not lie
Pr x 1-x
L =1, if 0 to x otherwise 0
a)...