State
which of the following are not the probability distributions
of a random variable. Give reasons for your answer.
(i)
-
X
0
1
2
P (X)
0.4
0.4
0.2
(ii)
-
X
0
1
2
3
4
P (X)
0.1
0.5
0.2
− 0.1
0.3
(iii)
-
Y
−1
0
1
P (Y)
0.6
0.1
0.2
(iv)
-
Z
3
2
1
0
−1
P (Z)
0.3
0.2
0.4
0.1
0.05
State which of the following are not the probability distributions of a random variable. Give reasons for your answer.
(i)
-
X
0
1
2
P (X)
0.4
0.4
0.2
(ii)
-
X
0
1
2
3
4
P (X)
0.1
0.5
0.2
− 0.1
0.3
(iii)
-
Y
−1
0
1
P (Y)
0.6
0.1
0.2
(iv)
-
Z
3
2
1
0
−1
P (Z)
0.3
0.2
0.4
0.1
0.05
It is
known that the sum of all the probabilities in a probability
distribution is one.
(i) Sum
of the probabilities = 0.4 + 0.4 + 0.2 = 1
Therefore, the given table is a probability distribution of random
variables.
(ii) It
can be seen that for X = 3, P (X) = −0.1
It is known that probability of any observation is not negative.
Therefore, the given table is not a probability distribution of
random variables.
(iii) Sum
of the probabilities = 0.6 + 0.1 + 0.2 = 0.9 ≠
1
Therefore, the given table is not a probability distribution of
random variables.
(iv) Sum
of the probabilities = 0.3 + 0.2 + 0.4 + 0.1 + 0.05 = 1.05 ≠
1
Therefore, the given table is not a probability distribution of
random variables.
It is known that the sum of all the probabilities in a probability distribution is one.
(i) Sum of the probabilities = 0.4 + 0.4 + 0.2 = 1
Therefore, the given table is a probability distribution of random variables.
(ii) It can be seen that for X = 3, P (X) = −0.1
It is known that probability of any observation is not negative. Therefore, the given table is not a probability distribution of random variables.
(iii) Sum of the probabilities = 0.6 + 0.1 + 0.2 = 0.9 ≠ 1
Therefore, the given table is not a probability distribution of random variables.
(iv) Sum of the probabilities = 0.3 + 0.2 + 0.4 + 0.1 + 0.05 = 1.05 ≠ 1
Therefore, the given table is not a probability distribution of random variables.
