Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Suppose that a box contains 6 cameras and that 4 of them are defective. A sample of 2 cameras is selected at random, with replacement. Define the random variable
as the number of defective cameras in the sample.

Write the probability distribution for X.


What is the expected value of X
?

Sagot :

TiltedLunar

1. Probability distribution:

  P(X = 0) = (2/6) * (2/6) = 4/36 = 1/9

  P(X = 1) = (4/6) * (2/6) + (2/6) * (4/6) = 16/36 = 4/9

  P(X = 2) = (4/6) * (4/6) = 16/36 = 4/9

2. Expected value calculation:

  E(X) = 0 * P(X=0) + 1 * P(X=1) + 2 * P(X=2)

       = 0 * (1/9) + 1 * (4/9) + 2 * (4/9)

       = 0 + 4/9 + 8/9

       = 12/9

       = 4/3

Therefore, the expected value of X is 4/3 or approximately 1.33 defective cameras in the sample.

We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.