Question

Creating a Discrete Probability Distribution Table

Suppose that a box contains 7 cameras and that 4 of them are defective. A sample of 2 cameras is selected at random. Define the random variable X X as the number of defective cameras in the sample.

Write the probability distribution for X X .

Give your answers to 2 decimal places. k P(X = k)

What is the expected value of X X ? Give your answer to 2 decimal places.

Answer 1

Answer:

Given,

P(X = x) = 4Cx*3C(2-x) / 7C2

where as x = 0,1,2

P(x = 0) = 4C0*3C2/7C2

= 0.1429

P(x = 1) = 4C1*3C1/7C2

= 0.5714

P(x = 2) = 4C2*3C0/7C2

= 0.2857

x	0	1	2
P(x)	0.1429	0.5714	0.2857

E(X) = x*p(x)

= 0*0.1429 + 1*0.5714 + 2*0.2857

= 0 + 0.5714 + 0.5714

= 1.1428