Question

Let X and Y be two normal random variables, with means 0 and 3 , respectively, and variances 1 and 16 , respectively. Find the following, using the standard normal table. Express your answers to an accuracy of 3 decimal places.

1. P(X>−1)=

2. P(X≤−2)

3. Let V=(4−Y)/3 . Find the mean and the variance of V .

4. E[V]=

5. Var(V)=

6. P(−2<Y≤2)=

Answer 1

Let X and Y be two normal random variables, with means 0 and 3 , respectively, and variances 1 and 16 , respectively. Find the following, using the standard normal table. Express your answers to an accuracy of 3 decimal places.

1. P(X>−1)=0.841
2. P(X≤−2)=0.023

3. Let V=(4−Y)/3 . Find the mean and the variance of V .

4. E[V]=0.333

5. Var(V)=1.778

6. P(−2<Y≤2)=

Answer 2

6. P(−2<Y≤2)= 0.2957