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State which of the following are not the probability distributions of a random variable. Give reasons for your answer.
X | 0 | 1 | 2 | 3 | 4 |
P(X) | 0.4 | 0.5 | 0.2 | -0.1 | 0.3 |
Given: A given table with values for X and P(X).
As we see from the table that P(X) = -0.1 for X = 3.
It is known that probability of any observation must always be positive that it can’t be negative.
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)