1. ## Uniform Distribution

Sorry, im no good with LaTex :-(

Let Y be a random variable with the uniform distribution:

Y~U(2,10)

(a) What is E(Y)

(b) What is the standard deviation of Y?

(c) Input the CDF fy(Y) for y in the range 2 <or equal to y <or equal to 10?

(d) What is the probability that Y<8?

(e) What is the probability that 7 < Y < 8?

2. Originally Posted by sirellwood
Sorry, im no good with LaTex :-(

Let Y be a random variable with the uniform distribution:

Y~U(2,10)

(a) What is E(Y)

(b) What is the standard deviation of Y?

(c) Input the CDF fy(Y) for y in the range 2 <or equal to y <or equal to 10?

(d) What is the probability that Y<8?

(e) What is the probability that 7 < Y < 8?
What have you tried? Where are you stuck? Do you know what the pdf is that you need to use?

3. Im pretty sure part (a) = 6, part (b) = 2.309.... (i was just checking these before moving on).

For part (c), is it just 1, because it should cover the whole range between 2 and 10?

part (d) confused me because it is just less than rather than less than or equal to, and same with part (e)

4. Originally Posted by sirellwood
Im pretty sure part (a) = 6, part (b) = 2.309.... (i was just checking these before moving on).

For part (c), is it just 1, because it should cover the whole range between 2 and 10?

part (d) confused me because it is just less than rather than less than or equal to, and same with part (e)
(a) looks OK. For (b) an exact answer can surely be found (your answer is correct to three decimal places).

I don't know what (c) means.

(d) $\Pr(Y < 8) = \frac{1}{8} \int_2^8 dy$ (or just use basic geometry and get the area of a rectangle).

(e) $\Pr(7 < Y < 8) = \frac{1}{8} \int_7^8 dy$ (or just use basic geometry and get the area of a rectangle)

5. Thank You :-)