#### Question

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)

#### Solution

**(i) **It is known that the sum of probabilities of a probability distribution of random variables is one.

*k* = − 1 is not possible as the probability of an event is never negative.

`:.k = 1/10`

**(ii)** P (X < 3) = P (X = 0) + P (X = 1) + P (X = 2)

**(iii)** P (X > 6) = P (X = 7)

**(iv)** P (0 < X < 3) = P (X = 1) + P (X = 2)

Is there an error in this question or solution?

Solution A Random Variable X Has the Following Probability Distribution. Determine K, P (X < 3), P (X > 6), P (0 < X < 3) Concept: Random Variables and Its Probability Distributions.