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1

State which of the following are not the probability distributions of a random variable. Give reasons for your answer.

X | 0 | 1 | 2 |

P(X) | 0.4 | 0.4 | 0.2 |

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 = 0.4 + 0.4 + 0.2

= 1

Hence, the given table is the probability distributions of a random variable.

1

8

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 | K | 2 K | 7 K |

Determine

(i) k (ii) P(X < 3)

(iii) P(X > 6) (iv) P(0 < X < 3)