A company receives shipments from two factories. Depending on the size of the order, a shipment can be in 1 box for a small order, 2 boxes for a medium order, 3 boxes for a large order. The company has two different suppliers. Factory Q is 60 miles from the company. Factory R is 180 miles from the company. An experiment consists of monitoring a shipment and observing B, the number of boxes, and M, the number of miles the shipment travels. The following probabity model describes the experiment:

Factory Q Factory R
small order 0.3 0.2
medium order 0.1 0.2
large order 0.1 0.1

a. Find PB M(b, m), the joint PMF of the number of boxes and the distance.
b. What is E[B], the expected number of boxes?
c. Are B and M independent?

Answers

Answer 1

Answer:

A) PB M(b, m), we have;

b = 1

b = 2

b = 3

B) E(B) = 1.7

C) No they are not independent

Step-by-step explanation:

A) We are told that a shipment can be in 1 box for a small order, 2 boxes for a medium order, 3 boxes for a large order. Thus;

For PB M(b, m), we have;

b = 1

b = 2

b = 3

B) Factory Q is 60 miles from the company. Thus, under factory Q in the table, m = 60

Factory R is 180 miles from the company. Thus under factory R in the table, m = 180

Now;

P_B (b) for b = 1 which is small order is;

P_B (b) = 0.3 + 0.2 = 0.5

P_B (b) for b = 2 which is medium order is;

P_B (b) = 0.1 + 0.2 = 0.3

P_B (b) for b = 3 which is large order is;

P_B (b) = 0.1 + 0.1 = 0.2

Thus;

E(B) = Σb•P_B (b) = (1 × 0.5) + (2 × 0.3) + (3 × 0.2)

E(B) = 0.5 + 0.6 + 0.6

E(B) = 1.7

C) No, they are not independent. This is because from the table we are given, P_B,M at b = 1 and m = 60 is given as 0.3.

Whereas, for B and M to be independent, P_B,M at b = 1 and m = 60 has to be equal to (P_M(m) under m = 0.3) multiplied by P_B(b) for b = 1.

Instead what we have is P_M(m) under m = 0.3 as; 0.3 + 0.1 + 0.1 = 0.5. Which means (P_M(m) under m = 0.3) multiplied by P_B(b) for b = 1 gives;

0.5 × 0.5 = 0.25 which is not equal to P_B,M = 0.3 at b = 1 and m = 60


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Answer:

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Answer:

Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

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Step-by-step explanation:

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have a great day :D

Answer:  50 + 50x

========================================================

Explanation:

To get this answer, we multiply the outer term 10 by each term inside

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I'm using the distribution rule or distributive property. So that's why (5+5x)10 is the same as 50+50x

We could arrange the terms to get 50x+50 if you wanted.

--------------------------

Extra info (optional section):

Let's say that instead of 10, we had a smaller value like 2

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Answers

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation

Easy!

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Answers

Answer:

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Trust

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