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State which of the following are not the probability distributions of a random variable. Give reasons for your answer.
Z | 3 | 2 | 1 | 0 | -1 |
P(Z) | 0.3 | 0.2 | 0.4 | 0.1 | 0.05 |
Given: A given table with values for X and P(X).
As we know the sum of all the probabilities in a probability distribution of a random variable must be one.
Hence the sum of probabilities of given table = 0.3 + 0.2 + 0.4 + 0.1 + 0.05
= 1.05 ≠ 1
Hence, the given table is not the probability distributions of a random variable.
A random variable X has the following probability distribution:
X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
P(X) | 0 | k | 2k | 2k | 3k | K2 | 2 K2 | 7 K2 + k |
Determine
(i) k (ii) P(X < 3)
(iii) P(X > 6) (iv) P(0 < X < 3)