Continuous random variable question

[dylbester]

A continuous random variable x has the following probability function:
f(X)=(X+1)/8
-1<=X<=3
0 Otherwise

1. Find the Pr(X<=2)
2. Find the mean of X

 

[MarkFL]

Hello and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far, here and in your other threads?

 

[dylbester]

mean of X is defined as ∫ x * f (x) dx over the domain of definition of X
∫ x (x + 1) / 8 dx
= ∫ (x^2 + x) / 8 dx
= x^3 / 24 + x^2 / 16 + c
Over the interval [-1, 3], we get:
(3^3 - (-1)^3) / 24 + (3^2 - (-1)^2) / 16
= 7/6 + 1/2
= 5/3

Im I right?

 

[Siron]

Your calculation of the expected value (=mean) is correct. Have you already figured out how to compute $\mathbb{P}(X \leq 2)$?

Hint: use the link between a probability and the area under a density function