Discrete Random Variables A discrete random variable is

Discrete Random Variables A discrete random variable is a numerical value that can only take particular values (discrete - e. g. number of televisions in a household, score obtained from rolling a dice - NOT height which is measured on a continuous scale). The value is obtained by taking a measurement from a real life experiment where the results are not chosen (random) and can vary (not always the same result. ) • • Capital letters like X and Y are used to denote the random variable Small letters like x and y are used to denote particular values of the random variable Example: A dice is rolled 4 times. The number of times it lands on a 6 is noted, denoted Y. Write down the possible values of Y. Y is the random variable “number of times in 4 rolls a dice lands on a 6” y is the possible number of times the dice can land on a 6 Therefore, possible values of Y are JP

• 1 2 3 4 0. 25 JP This total must … must

• 1 2 3 4 5 0. 1 0. 2 0. 15 0. 25 0. 3 JP

• 1 2 3 4 5 0. 1 0. 2 0. 15 0. 25 0. 3 1 2 3 4 5 0. 1 0. 3 0. 45 0. 7 1 Note that F(2. 2) = F(2. 7) = F(2. 9) etc JP

Mean and Variance of a Discrete Random Variable • -2 -1 1 2 JP Ex 8 c Q 2, 3, 5 Ex 8 d Q 1, 6, 7, 4

More on Expectation and Variance • JP Ex 8 E Q 2, 6, 7, 8