Question

Suppose that a box contains 7 cameras and that 5 of them are defective. A sample of 2 cameras is selected at random without replacement. Define the random variable

X
as the number of defective cameras in the sample.

Answer 1

E(x) = 1.43 (Approx)

Explanation:

Given:

Total number of camera = 7

Defective camera = 5

Sample selected = 2

Computation:

when x = 0

P(x=0) = 2/7 × 1/6 = 2/42

P(x=1) = [2/7 × 5/6] + [5/7 × 2/6] = 20/42

P(x=2) = 5/7 × 4/6 = 20/42

So,

E(x) = [0×2/42] + [1×20/42] + [2×20/42]

E(x) = 1.43 (Approx)