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)

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

the answer would be 150 books

step-by-step explanation:

if you divide 300 by 2 you will get 150