Discrete random variables and their distributions

Three quick questions from earlier lessons.

X is the number of heads in two coin tosses. Its values are 0, 1, 2. Which list gives their probabilities?

A random variable assigns a number to each outcome.

A discrete random variable

X

has a list of values with probabilities

P(X = x)

. Every probability is between 0 and 1, and they sum to 1. Probabilities of events such as

X \ge 2

add the matching values.

$P(X = 0) = 0.2$ , $P(X = 1) = 0.5$ , $X$ takes only 0, 1, 2.

P(X = 2) = 1 - 0.2 - 0.5 = 0.3

Sum to 1.

P(X \ge 1) = 0.8

Everything but 0.

Your turn: $P(X = 0) = 0.1$ , $P(X = 1) = 0.6$ . Find $P(X = 2)$ .

0.3

1 − 0.1 − 0.6.

A random variable X takes the values 0, 1 and 2, with P(X = 0) = 29/100 and P(X = 1) = 13/100. Find P(X = 2).
A random variable X takes the values 0, 1 and 2, with P(X = 0) = 14/100 and P(X = 1) = 18/100. Find P(X = 2).

Which list could be the probabilities of a random variable with three values?
1. 0.1, 0.5 and 4/10
2. 0.5, 0.5 and 0.1
3. 0.8, 0.4 and −0.2

X takes the values 0, 1, 2 with P(X = 0) = 25/100 and P(X = 1) = 15/100. Find P(X ≥ 1).
X takes the values 0, 1, 2 with P(X = 0) = 34/100 and P(X = 1) = 15/100. Find P(X ≥ 1).

Three questions to check you have got it.

A random variable X takes the values 0, 1 and 2, with P(X = 0) = 29/100 and P(X = 1) = 13/100. Find P(X = 2).
A random variable X takes the values 0, 1 and 2, with P(X = 0) = 14/100 and P(X = 1) = 18/100. Find P(X = 2).
A random variable X takes the values 0, 1 and 2, with P(X = 0) = 18/100 and P(X = 1) = 23/100. Find P(X = 2).

Discrete distributions

Watch out: values are not automatically equally likely.

End of the lesson