When an automobile is stopped with a roving safety patrol, each tire is checked for tire wear, and each headlight is checkedto see whether it is properly aimed. Let X denote the numberof headlights that need adjustment, and let Y denote the numberof defective tires.

a) if X and Y are independent with Px(0) = .5, Px(1) =.3,Px(2) =.2 and Py(0) =.6, Py(1) =.1, Px(2) =Py(3) =..05, Py(4) =.2,display the joint probability distribution table.
b) compute P(X<= 1 and Y <= 1) fromthe joint probability distribution table and verify that it isequals to the product P(X <= 1) * P(Y<=1)
c) What is P(X+Y = 0) (theprobability of no violations)?
d) Compute P(X + Y <= 1).

a) Joint ptobability distribution

b) P(X<= 1 and Y <= 1) = P(X<= 1) * P(Y<=1) = 0.56

c) P(X + Y = 0)=0.3

d) P(X + Y <= 1)=0.53

Step-by-step explanation:

We have to construct the joint probability table with the marginal probabilities of X and Y.

X can take values from 0 to 2, and Y can take values from 0 to 4.

We can calculate each point of the joint probability as:

Then, the joint probabilities are:

X=0Y=0Px=0.5Px=0.6P(0,0)=0.3

X=0Y=1Px=0.5Px=0.1P(0,1)=0.05

X=0Y=2Px=0.5Px=0.05P(0,2)=0.025

X=0Y=3Px=0.5Px=0.05P(0,3)=0.025

X=0Y=4Px=0.5Px=0.2P(0,4)=0.1

X=1Y=0Px=0.3Px=0.6P(1,0)=0.18

X=1Y=1Px=0.3Px=0.1P(1,1)=0.03

X=1Y=2Px=0.3Px=0.05P(1,2)=0.015

X=1Y=3Px=0.3Px=0.05P(1,3)=0.015

X=1Y=4Px=0.3Px=0.2P(1,4)=0.06

X=2Y=0Px=0.2Px=0.6P(2,0)=0.12

X=2Y=1Px=0.2Px=0.1P(2,1)=0.02

X=2Y=2Px=0.2Px=0.05P(2,2)=0.01

X=2Y=3Px=0.2Px=0.05P(2,3)=0.01

X=2Y=4Px=0.2Px=0.2P(2,4)=0.04

We can write it in the form of a matrix:

b) From the joint probability P(X<= 1 and Y <= 1) is equal to

We can calculate P(X<= 1) * P(Y<=1)

Both calculations give the same result.

c) Probability of no violations

d) P(X + Y <= 1)

maybe showing the graph would

step-by-step explanation:

-387129 iq

javeir earned 56 dollors more than kyle so kyle and javier had 14w but javier made 56 dollors more so 14w plus 56 equals 70w so kyle has 14w

step-by-step explanation: hope i plz give me brainliest with the points so this is not constant cause it says last week so its clearly not every week