Calculating Probability for a Discrete Random Variable

[bethanyd]

Homework Statement

If X is a discrete random variable with p.d.f. f(x) = {cx if x=1,2,3,4 ; 0 otherwise} where c is a constant.
Find P(1< X =< 3.5)

Homework Equations

I solved for c:
f(x) = 1 = c(1+2+3+4)
10c = 1
c = 1/10

The Attempt at a Solution

I have the following solution:
P(1< X =< 3.5) = f(3.5) - f(1)
= c(3.5) - c(1)
= c(2.5)
=0.25

I am not sure if this is correct. Please help!

Beth

 

[roadrunner]

f(x) = 1 = c(1+2+3+4) why ?
isnt it integral of f(x)=1?
i could be totaly off though!

 

[bethanyd]

hmm, possibly... we're not supposed to use calc in my course, or would there be another way of solving it?

 

[roadrunner]

no idea, I am in a class too, and apparently i have to do that to somethign with 2 variables, and I am so confused! :P sorry i can't help more

 

[bethanyd]

aw, no problems... this question is so frustrating because it's really difficult to find examples online, and I don't think we did a single example in class of this. I don't want to just guess the answer, but I may have to!

 

[EnumaElish]

Homework Statement

If X is a discrete random variable with p.d.f. f(x) = {cx if x=1,2,3,4 ; 0 otherwise} where c is a constant.
Find P(1< X =< 3.5)

Homework Equations

I solved for c:
f(x) = 1 = c(1+2+3+4)
10c = 1
c = 1/10

The Attempt at a Solution

I have the following solution:
P(1< X =< 3.5) = f(3.5) - f(1)
= c(3.5) - c(1)
= c(2.5)
=0.25

I am not sure if this is correct. Please help!

Beth

X is discrete. It can only take on integer values 1, 2, 3, 4. You are violating this condition in your calculation.

Does this help?