- #1
Dassinia
- 144
- 0
Hello, I am stuck at this exercise:
1. Homework Statement
X ~ U(0, a), a > 0 and Y = min(X; a=2).
- Find the cumulative distribution function of Y
-Is the variable Y continuous ?
3. The Attempt at a Solution [/B]
The density function for X is
f(t)= 1/a if 0≤t≤a , 0 elsewhere
Is it correct to write that :
∀t < 0, P(Y ≤ t) = 0
∀0 ≤ t < a/2, P(Y ≤ t) = P(X ≤ t) = t/a
∀t ≥ a/2, P(Y ≤ t) = 1
And then don't know what to do
Thanks
1. Homework Statement
X ~ U(0, a), a > 0 and Y = min(X; a=2).
- Find the cumulative distribution function of Y
-Is the variable Y continuous ?
Homework Equations
3. The Attempt at a Solution [/B]
The density function for X is
f(t)= 1/a if 0≤t≤a , 0 elsewhere
Is it correct to write that :
∀t < 0, P(Y ≤ t) = 0
∀0 ≤ t < a/2, P(Y ≤ t) = P(X ≤ t) = t/a
∀t ≥ a/2, P(Y ≤ t) = 1
And then don't know what to do
Thanks