Course

ConceptRandom Variables and Its Probability Distributions

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#### Questions

Probability distribution of X is given by

X = x | 1 | 2 | 3 | 4 |

P(X = x) | 0.1 | 0.3 | 0.4 | 0.2 |

Find P(X ≥ 2) and obtain cumulative distribution function of X

State 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 |

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

X | 0 | 1 | 2 | 3 | 4 |

P(X) | 0.1 | 0.5 | 0.2 | -0.1 | 0.3 |

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

Y | -1 | 0 | 1 |

P(Y) | 0.6 | 0.1 | 0.2 |

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} |
2 |
7k^{2} + k |

Determine

**(i)** *k*

**(ii)** P (X < 3)

**(iii)** P (X > 6)

**(iv)** P (0 < X < 3)

**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 |