The Binomial Distribution Worksheet (Page 2 of 6) in pdf

The Binomial Distribution Worksheet Page 2

Example (based on Example 4.10, p. 201) A computer retailer sells both desktop and laptop

personal computers (PCs) online. Assume that 80% of the PCs that the retailer sells online are

desktops and 20% are laptops, and that sells are independent. Let x represent the number of the

next four online PC purchases that are laptops.

1. Explain why x is a binomial random variable; state what is the success, what is the

failure, and what are the values of p, q, and n. What are possible values of x

2. Derive formula for the probability distribution p(x) of x.

3. Find the expected value and the standard deviation of x.

Extend (guess) the formula for p(x) to the case of an arbitrary Binomial experiments with

arbitrary n and p.

SOLUTION

1. Success = a laptop is purchased (L), failure = a desktop is purchased (D),

p=P(L)=0.20,

q=P(D)=1-p=0.80,

n=4, x = 0, 1, 2, 3, 4

x =

P(a sample point ) =

(.8)

(.2)

(.8)

(.2)

(.8)

(.2)

(.8)

(.2)

# of sample points=

P(x=0) = (.8)

0.4096

P(x=1) = 4

(.2)

(.8)

= 0.4096

P(x=2) = 6

(.2)

(.8)

= 0.1536

P(x=3) = 4

(.2)

(.8)

= 0.0256

P(x=4) = (.2)

= 0.0016

The Binomial Distribution Worksheet Page 2