A company has five warehouses, only two of which have a particular product in stock. A salesperson calls the five warehouses in a random order until a warehouse with the product is reached. Let the random variable X be the number of calls made by the salesperson, and calculate its probability mass function and cumulative distribution function.
Answers
Given : A company has five warehouses, only two of which have a particular product in stock. A salesperson calls the five warehouses in a random order until a warehouse with the product is reached
To Find : probability mass function and cumulative distribution function.
Solution:
Calls made = 1
then Chances = 2/5 = 0.4
calls made = 2
X = 2
1st call from 3 and 2nd call from 2
(3/5)(2/4) = 3/10 = 0.3
=
calls made = 3
1st 2 calls from 3 and 3rd call from 2
(3/5)(2/4)(2/3) = 1/5 = 0.2
calls Made = 4
1st 3 calls from 3 and 4th call from 2
(3/5)(2/4)(1/3)(2/2) = 1/10 = 0.1
P(X) = probability mass function
F(X) = cumulative distribution function.
X P(X) F(x) = P( x ≤ X)
1 0.4 0.4
2 0.3 0.7
3 0.2 0.9
4 0.1 1
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