Question

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 ?

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