In: Math
When an automobile is stopped by a roving safety patrol, each tire is checked for tire wear, and each headlight is checked to see whether it is properly aimed. Let X denote the number of headlights that need adjustment, and let Y denote the number of defective tires.
(a) If X and Y are independent with pX(0) = 0.5, pX(1) = 0.3, pX(2) = 0.2, and pY(0) = 0.1, pY(1) = 0.2, pY(2) = pY(3) = 0.05, pY(4) = 0.6, display the joint pmf of (X, Y) in a joint probability table.
y | ||||||
p(x, y) |
0 | 1 | 2 | 3 | 4 | |
x | 0 | |||||
1 | ||||||
2 |
(b) Compute P(X ≤ 1 and Y ≤ 1) from the
joint probability table.
P(X ≤ 1 and Y ≤ 1) =
Does P(X ≤ 1 and Y ≤ 1) equal the
product P(X ≤ 1) · P(Y ≤
1)?
YesNo
(c) What is P(X + Y = 0) (the
probability of no violations)?
P(X + Y = 0) =
(d) Compute P(X + Y ≤ 1).
P(X + Y ≤ 1) =