Discrete probability distributions

 

Below is a probability table

xi	0	1	2	3
P(X = xi)	4c	5c	8c	13c

(a) Find the value of c.
(b) Confirm it is a probability distribution.
(C) What is P(X > 1)?

Probabilities must sum to 1, so

\[ \begin{align} 1 &= 4c + 4c + 8c + 13c \\ 1 & = 30c \\ c &= \frac{1}{30} \end{align}\ \]

Check by substituting

\[ \begin{align} \frac{4}{30} + \frac{5}{30} + \frac{8}{30} + \frac{13}{30} &= 1 \\ \end{align} \ \] and all probabilities are non-negative.

Add the probabilities for 2 and three.

\[ \begin{align} P(X \gt 1) &= (P(X = 2) + P(X = 3)) \\ &= \frac{8}{30} + \frac{13}{30} \\ &= \frac{21}{30} \end{align}\ \]

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What property of a probability distribution do you need to use?

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Now You Try:

Above is a probability table

(a) Find the value of c.
(b) Confirm it is a probability distribution.
(C) What is P(X < 3)?

 

Probabilities are discrete
Probabilities are greater than zero
Probabilities must sum to 1