The following density function describes a random variable x. f(x) = 1 − (x /2) if 0

a. Find the probability that X is greater than 1: _P(X>1) = 0.25

b. Find the probability that X is less than .5: _P(X<0.5)_

c. Find the probability that X is equal to 1.5:  P(X=1.5)= 0

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!

c is the final answer! : )

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step-by-step explanation: