Question

In: Math

When an automobile is stopped by a roving safety patrol, each tire is checked for tire...

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) =

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