Question

Which of the following tables shows a valid probability density function? Select all correct answers.

Select all that apply:

• x	P(X=x)
  0	14
  1	12
  2	14

• x	P(X=x)
  0	12
  1	18
  2	14
  3	18

• x	P(X=x)
  0	0.0
  1	0.02
  2	0.16
  3	0.0
  4	1.07

• x	P(X=x)
  0	0.89
  1	0.09
  2	0.0
  3	0.02
  4	0.0

• x	P(X=x)
  0	35
  1	25
  2	−110
  3	110

• x	P(X=x)
  0	110
  1	110
  2	310
  3	310

Answer 1

Solution:

A distribution is said to be a  valid probability density function, if each Probability is greater than or equal to 0 and total of all probabilities is 1.

That is: for all i = 1 ,2,3,4.......n

and

  

Thus from given tables we have:

x	P(X=x)
0	0.89
1	0.09
2	0.00
3	0.02
4	0.00
	1.00

Each probability is greater than or equal to 0 and total of all probabilities is 1.

Thus this table shows a valid probability density function.

All other tables have probabilities more than 1 and total is more than 1 , so all other tables are not valid probability density function.