1. ## Continuous Random Variables

Hi could anyone check if I have done the following questions correctly and also help me out with a couple:

The random variable X has N(2,3) distribution. Evaluate:

(i) P( X > 3 )
(ii) P(-1 < X < 4 )
(iii) Find a, such that P( (X-2) < a ) = 0.1

So for part (i) I have P(Z> (1/root3) )
and for part (ii) i have P( Z < (2/root3) - P (Z < -3/root3)

Second question is:

The random variables X and Y are independent N(1,5) and N(5,1).

Evaluate:
(i) P( X < 0, Y > 6) and
(ii) P ( -3 < 3X - Y < 0)

Thanks.

2. Originally Posted by axa121
Hi could anyone check if I have done the following questions correctly and also help me out with a couple:

The random variable X has N(2,3) distribution. Evaluate:

(i) P( X > 3 )
(ii) P(-1 < X < 4 )
(iii) Find a, such that P( (X-2) < a ) = 0.1

So for part (i) I have P(Z> (1/root3) )
and for part (ii) i have P( Z < (2/root3) - P (Z < -3/root3) Mr F says: Once you have the z-values you should have been taught how to use standard normal tables to get the required probabilities (look in your classnotes or textbook).

Second question is:

The random variables X and Y are independent N(1,5) and N(5,1).

Evaluate:
(i) P( X < 0, Y > 6) and
(ii) P ( -3 < 3X - Y < 0)

Thanks.
(i) Pr( X < 0) times Pr(Y > 6).

(ii) Since X and Y are independent, W = 3X - Y follows a normal distribution with mean 3E(X) - E(Y) and variance 3^2Var(X) + 1^2 Var(Y) (see property 1 here Normal distribution - Wikipedia, the free encyclopedia). So calculate Pr(-3 < W < 0) in the usual way.

3. Yep, I do have the tables. I just wanted to know whether the Z values were correct.

Thanks, I will the second question and post my answers.