solution10

# solution10 - Solutions to Homework 10 1 a P[|X| < 5 Y > 2 Z...

This preview shows pages 1–2. Sign up to view the full content.

1. a. P [ | X | < 5 , Y > 2 , Z 2 2] = P [ | X | < 5] P [ Y > 2] P [ Z 2 2] = P [ - 5 < X < 5](1 - P [ Y 2])(1 - P [ - 2 < Z < 2] = ( F X (5 - ) - F X ( - 5))(1 - F Y (2))(1 - F Z ( 2 - ) + F Z ( - 2)) b. P [ X > 5 , Y < 0 , Z = 1] = P [ X > 5] P [ Y < 0] P [ Z = 1] = (1 - F X (5)) F Y (0 - ))( F Z (1) - F Z (1 - )) c. P [min( X, Y, Z ) > 2] = P [ X > 2 , Y > 2 , Z > 2] = P [ X > 2] P [ Y > 2] P [ Z > 2] = (1 - F X (2))(1 - F Y (2))(1 - F Z (2)) d. P [max( X, Y, Z ) < 6] = P [ X < 6 , Y < 6 , Z < 6] = P [ X < 6] P [ Y < 6] P [ Z < 6] = F X (6 - ) F Y (6 - ) F Z (6 - ) 2. a. Summing up the rows and columns we get the marginal pmf’s i. ii. iii. X Y - 1 0 1 P Y ( y ) - 1 1 6 0 1 6 1 3 0 0 1 3 0 1 3 1 1 6 0 1 6 1 3 P X ( x ) 1 3 1 3 1 3 1 X Y - 1 0 1 P Y ( y ) - 1 1 9 1 9 1 9 1 3 0 1 9 1 9 1 9 1 3 1 1 9 1 9 1 9 1 3 P X ( x ) 1 3 1 3 1 3 1 X Y - 1 0 1 P Y ( y ) - 1 0 0 1 3 1 3 0 0 1 3 0 1 3 1 1 3 0 0 1 3 P X ( x ) 1 3 1 3 1 3 1 b. i

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

solution10 - Solutions to Homework 10 1 a P[|X| < 5 Y > 2 Z...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online