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Chapter 4: Q.4.57 (page 167)

Suppose that the number of accidents occurring on a highway each day is a Poisson random variable with parameter 位 = 3.

(a) Find the probability that 3 or more accidents occur today.

(b) Repeat part (a) under the assumption that at least 1 accident occurs today.

Short Answer

Expert verified

The probability that at least 3 accidents occur is 0.57681 while the probability that at least 3 accidents occur under the assumption that at least 1 accident occurs today is 0.60703.

Step by step solution

01

Step 1:Given Information (Part a)

The number of accidents occurring on a highway each day is a Poisson random variable with parameter位=3.

02

Step 2:Calculation (Part a)

P(X鈮�3)=1-鈭�i=023ii!e位

=1-300!e3+311!e3+322!e3

=0.57681.

03

Final answer (Part a)

The probability that at least 3accidents occur is0.57681.

04

Given Information (Part b)

The number of accidents occurring on a highway each day is a Poisson random variable with parameter 位=3.

05

Calculation (Part b)

P{(X鈮�3)鈭�(X鈮�1)}=P{(X鈮�3)鈭�(X鈮�1)}P{X鈮�1}

(X鈮�1)鈯�(X鈮�3)鈬�P{(X鈮�3)鈭�(X鈮�1)}P{X鈮�1}=P{X鈮�3}P{X鈮�1}

Substitute the given expression,

P{X鈮�3}P{X鈮�1}=0.576811-P{X=0}

=0.576811-e-3

=0.60703.

06

Final answer (Part b)

The probability that at least 1 accidents occur is 0.60703.

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