Answer:
a. Find the probability that X is greater than 1: _<u>P(X>1) = 0.25</u>
b. Find the probability that X is less than .5: _<u>P(X<0.5)</u>_
c. Find the probability that X is equal to 1.5: <u> P(X=1.5)= 0</u>
Step-by-step explanation:
Hello!
The following density function describes a random variable X. f(x) = 1 − (x /2) if 0<x<2 a. Find the probability that X is greater than 1 ________ b. Find the probability that X is less than .5. _________ c. Find the probability that X is equal to 1.5.
First step to calculate the asked probabilities is to integrate the density function.
f(x) = 1 − (x /2) if 0<x<2
Now you resolve both integrals:
=
The cummulative distribution is:
0 for x ≤ 0
for 0 < x < 2
1 for x ≥ 2
a. Find the probability that X is greater than 1.
P(X>1) = 1 - P(X ≤ 1)
"1" is included in the interval "0 < x < 2", to calculate the probability you have to replace it with and replace X with 1
1 - P(X ≤ 1) = 1 - ()= 1 - 075= 0.25
b. Find the probability that X is less than 0.5.
"0.5" in included in the interval "0 < x < 2", to calculate the probability you have to replace it with and replace X with 0.5
P(X<0.5)= = 0.4375
c. Find the probability that X is equal to 1.5.
"1.5" is included in the interval "0 < x < 2", to calculate the probability you have to replace it with and replace X with 1.5
This is a continuous variable, in this type of variable the cumulative probability of X=k (k= constant) is always cero.
You can prove it doing the following calculation:
= - () = 0
I hope it helps!