Question

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

Answer 1

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

Explanation:

Answer 2

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.