SOLUTION: <pre>Determine whether each of the distributions given below represents a probability distribution. Justify your answer. please walk me through this ----------- ----------- --

Algebra ->  Probability-and-statistics -> SOLUTION: <pre>Determine whether each of the distributions given below represents a probability distribution. Justify your answer. please walk me through this ----------- ----------- --      Log On


   



Question 703785:
Determine whether each of the distributions given below represents a probability distribution.    Justify your answer.
please walk me through this
----------------------------------
(A)
x    P(x)
1    1/5
2    9/25
3    2/5
4    1/25
----------------------------------
(B)
x   P(x)
3   0.7
6   1/12
8   0.22
----------------------------------
(C) 
 x    P(x)
20   13/25
30    0.25
40   -0.01
50    6/25

Answer by AnlytcPhil(1807) About Me  (Show Source):
You can put this solution on YOUR website!
We have to check just two requirements:

(1)   All the probabilities in the P(x)
list must be between 0 and 1 inclusive.

(2)   The sum of the probabilities in
the P(x) list must equal to 1.
----------------------------------
(A)
x    P(x)
1    1/5
2    9/25
3    2/5
4    1/25

It meets the requirements of (1). Let's
check requirement (2) 
1%2F5%2B9%2F25%2B2%2F5%2B1%2F25
Get LCD of 25
5%2F25%2B9%2F25%2B10%2F25%2B1%2F25 =
25%2F25 = 1, so yes it is a
probability distribution.
----------------------------------
(B)
x   P(x)
3   0.7
6   1/12
8   0.22
It meets the requirements of (1). Let's
check requirement (2) 

0.7%2B1%2F12%2B0.22
Change the decimals to fractions 
7%2F10%2B1%2F12%2B22%2F100 
Get LCD of 300
210%2F300%2B25%2F300%2B66%2F300

301%2F300 ≠ 1, so NO it is NOT a
probability distribution.
----------------------------------
(C) 
 x    P(x)
20   13/25
30    0.25
40   -0.01
50    6/25

It does NOT meet requirement (1), because of
the negative number in the probability list,
so it is NOT a probability distribution
function.

Edwin