Suppose that a box contains 6 cameras and that 3 of them are defective. A sample of 2 cameras is selected at random (with replacement). Define the random variable X as the number of defective cameras in the sample. Note: For X to have a binomial probability distribution the sample must be with replacement, otherwise the trials are dependent. Write the probability distribution for X. k P (X = k) 0 Correct. 2 Incorrect 1 Correct. 5 Correct 2 Correct. 2 Incorrect What is the expected value of X?

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11 June, 12:44

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Sonny Potts · Answer 1

p = 3/6 = 0.5

X ~ B (6, 0.5)

P (X=k) = 6Ck * 0.5^k * 0.5^ (6-k)

E (X) = np = 6 (0.5) = 3