Question

Which of the following distributions of probabilities of a random variable X are the probability distributions?
(i)

X :	3	2	1	0	−1
P (X) :	0.3	0.2	0.4	0.1	0.05

 

(ii)

X :	0	1	2
P (X) :	0.6	0.4	0.2

(iii)

X :	0	1	2	3	4
P (X) :	0.1	0.5	0.2	0.1	0.1

 

(iv)

X :	0	1	2	3
P (X) :	0.3	0.2	0.4	0.1

 

Answer 1

(i) P (X = 3) + P (X = 2) + P (X = 1) + P (X = 0) + P (X = -1)

  = 0.3 + 0.2 + 0.4 + 0.1 + 0.05
    =1.05 > 1
It is not the probability distribution of random variable X. 

(ii) P (X = 0) + P (X = 1) + P (X = 2)
     = 0.6 + 0.4 + 0.2
     = 1.2 > 1
It is not the probability distribution of random variable X.

(iii) P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4)
      = 0.1 + 0.5 + 0.2 + 0.1 + 0.1
      = 1
It is the probability distribution of random variable X.

(iv) P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3)
      = 0.3 + 0.2 + 0.4 + 0.1
      = 1
It is the probability distribution of random variable X.