I\'m really stuck in this problem, any help would be really appreciated, Thanks!
ID: 3289917 • Letter: I
Question
I'm really stuck in this problem, any help would be really appreciated, Thanks!
Consider the following cumulative distribution function F(x) for x€0.2 F(T 0.5 0 0.5 1 1.5 2 lc a. Write down the density function f(x) corresponding to this F(x). Do not sketch a graph of f, but rather specify its values on appropriate interval:s b. State whether a random variable with this distribution has positive or negative expectation. Justify your answer in a couple of words c. Compute the probability of the event A {w: X(a) E (0.6, 0.65 }. Is it possible for a random variable to be distributed according to the c.d.f pictured below? Justify your answer. F(T 0.5 0 0.5 1.5 2'*Explanation / Answer
F(x) =
{ x 0 < x< 0.5
0.5 0.5 <x< 1.5
x-0.5 1.5 <x< 2
f(x) = d/dx (F(x)
hence
f(x) = {
1 0 <x<0.5
0 0.5 <x< 1.5
1 1.5 <x< 2
b) E(X) > 0 this is because every value od pdf is positive
c) P(A) = 0
as P(0..5 <X< 0.65)= 0
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