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The probability equation for a survey on the number of speeding tickets given on a certain day in a local neighborhood is given as p(x) = 7-2x/20 (where x can be 0,1,2, or 3). does this determine a probability distribution why or why not

User DownChapel
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2 Answers

5 votes

Answer:

I belive the answer is no because the sum is not equal to 1


Explanation:


User Sparkitny
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4 votes

Solution:

The probability equation for a survey on the number of speeding tickets given on a certain day in a local neighborhood is given as p(x) =
(7-2 x)/(20) ,where x = 0,1,2, or 3.


P(0)=(7-2*0)/(20)=(7)/(20)\\\\P(1)=(7-2*1)/(20)=(5)/(20)=(1)/(4)\\\\P(2)=(7-2*2)/(20)=(3)/(20)\\\\ P(0)=(7-2*3)/(20)=(1)/(20)

As, variables are discrete ,it is the case of discrete probability distribution. And x, takes the value, =0,1,2,3

Sum of these values must be equal to 1.

So, P(0) +P(1)+P(2)+P(3)
=(7)/(20)+(5)/(20)+(3)/(20)+(1)/(20)\\\\ =(16)/(20)\\\\=(4)/(5)

≠ 1

So, it is not a Probability distribution.As, sum of Probabilities of each x, value is not equal to 1.

User Tomasz Ferfecki
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