Question

1. Determine whether the distribution represents a probability distribution.

X	3	7	9	12	14
P(X)	4/13	1/13	3/13	1/13	2/13

2. Determine whether the distribution represents a probability distribution.

X 5 7 9

P(X) 0.6 0.8 -0.4

3. Determine whether the distribution represents a probability distribution.

X 20 30 40 50

P(X) 0.05 0.35 0.4 0.2

Answer 1

Probability distribution is valid if

i) Probability values are between 0 and 1 inclusive.

ii) Sum of probabilities are equal to 1.

1)

All probbailities are between 0 and 1, Now check whether sum equal to 1.

P(X) = 4/13 + 1/13 + 3/13 + 1/13 + 2/13

= 11/13 1

This is not probability distribution.

2)

Since one of the probability value is negative, this is not probability distribution.

3)

All probability values are between 0 and 1 .

Now,

P(X) = 0.05 + 0.35 + 0.4 + 0.2

= 1

This is probability distribution.