1. -/19 points When an automobile is stopped by a roving safety patrol, each tir

Question

1. -/19 points 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. + DevoreStat9 5..50 1.XP My Notes Ask Your Teacher (a) If X and Yare independent with PX(0) = O 5, PX(1) = 0 3, px(2) Y) in a joint probability table. .2, and py(O) = 0.1. pr(1) p (2) = pa o o o A) o.i isplay theo ntp nfof X 0 2 (b) Compute P(X 1 and Y 1) from the joint probability table. P(X S 1 and YSI) Does P(X 1 and Y 1) equal the product P(X 1) . P(Y s 1)? Yes No (c) What is P(X + Y= 0) (the probability of no violations)? (d) Compute P(X +Y1) Need Help? Read It Talk to a Tutor

Explanation / Answer

Answer:

As per, given data as follows bellow.

(A)

(B)

P(X < = 1 and Y < = 1) = P(0,0) + P(1,0) + P(0,1) + P(1,1)

= 0.05 + 0.1 + 0.03 + 0.06

= 0.24

P(X<= 1) = 0.3

P(Y < = 1) = 0.8

P(X < = 1) * P(Y < = 1) = 0.24

(C)

P(X + Y = 0)

= P(0,0)

= 0.05

(D)

P(X + Y < = 1) = P(0,0) + P(1,0) + P(0,1)

= 0.05 + 0.1 + 0.03

= 0.1

p(x,y) 0 1 2 3 4 Total 0 0.05 0.1 0.025 0.025 0.3 0.5 1 0.03 0.06 0.015 0.015 0.18 0.3 2 0.02 0.04 0.01 0.01 0.12 0.2 Total 0.1 0.2 0.05 0.05 0.6 1

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