Maths(四)---Probability and Statistics(8)

Poisson Distribution

The probability distribution for a Poisson random variable X iS

例一.

A manufacturer of a certain type of LCD-screen finds that the number of “deadspots” on a screen is a Po(0.8) random variable. A screen with more than 3 “deadspots” has to be sold at a discount. Find the proportion of screens that are sold at a discount.

Solution

Let X be the number of “dead spots” on a screen. Then X ~ Po(0.8).

The proportion of screens that are sold at a discount

= P( X > 3)

= 1 – p(0) – p(1) – p(2) – p(3)

= 0.00908

例二.

A radio active source is emitting α-particles at an average of 2.6 particles per minute.Find the probability that the number of particles emitted in one minute is

(a) 0

(b) 1

(c) more than 1

Solution

Let X be the number of particles emitted in one minute.

(c) P(X > 1) = 1 – 0.0743 – 0.193 = 0.7327

Poisson Approximation to Binomial Distribution

A rule of thumb for the conditions under which this approximation may be used is

n ≥ 100, np <>

例一.

A company ships memory chips in boxes of 200. It is known that 0.001 of all thechips are defective. Find the probability that less than 3 chips in a box aredefective.

Solution
Let X be the number of defective chips in a box. Then X ~ Bin(200, 0.001).The average number of defective chips in a box = 200 × 0.001 = 0.2The distribution of X may be approximated by Po(0.2).