Question

The probability density of a random variable X is given in the following figure.

Answer 1

From this density, the probability that X is between 0.5 and 1.5 is
A. 1/3.
B. 1/2.
C. 3/4.
D. 1.
7. The density curve for a continuous random variable X has which of the following properties?
A. The probability of any event is the area under the density curve and above the values of X that make up the event.
B. The total area under the density curve for X must be exactly 1.
C. The probability of any event of the form X = constant is 0.
D. All of the above.

Answer 2

The probability that X is between 0.5 and 1.5 is found from the proportion of the total area between 0 and 2 that is found between 0.5 and 1.5.
For example the probability that X is between 0 and 0.5 is found from the proportion of the total area between 0 and 2 that is found between 0 and 0.5. This is found from the following proportion:
\[\frac{0.5}{2}=0.25\]
Can you find the answer to the first section now?

Answer 3

I would say 1/2 for tghe first part.

Answer 4

not too sure aobut the second part @kropot72

Answer 5

Three of the choices are clearly incorrect. Can you work on the basis of elimination? For example with choice A is it likely that the area above the values of X that make up the event would define the probability of the event?

Answer 6

It's not d.

Answer 7

I don't think it's c...

Answer 8

and I don't think it's a.... So B?

Answer 9

You are correct in finding that the answer to the first part is 1/2. Yes, B is the correct choice for the second part. Good work!

Answer 10

Thanks... Btw are you any good at linear algebra? I need to finish my last Q, I've been working on this for 15 hours :(.

http://openstudy.com/study#/updates/509739b7e4b0d0275a3d0cc9

Answer 11

if not onto the next stats Q http://openstudy.com/study#/updates/50973ef1e4b0d0275a3d0e97

Answer 12

:)

Answer 13

You're welcome :)
Linear algebra is not a strong point with me. Sorry.