Question

Think of some discrete random variable you observe on a regular basis. For example, it could be the (rounded) number of hours you sleep, how many gallons of gas are in your car when you get into it, how many boxes of cereal are in your house, how many days between grocery shopping, etc. (just make sure it takes only integer values). Try to list all of the possible values that this discrete random variable can take. If you can, collect some frequency data – give the relative frequency table and use this as an estimate of the probability distribution. Calculate the expected value and the standard deviation for this probability distribution. Interpret these parameters, and discuss whether they make sense based on your experience.

Answer 1

number of boys out of 3 kids in a house.

Possible values for discrete random variable x = 0, 1 , 2 , 3

Table for probabilities of discrete random variable:

x P(x) x*P(x) x²*P(x)

0 0.125 0 0

1 0.375 0.375 0.375

2 0.375 0.75 1.5

3 0.125 0.375 1.125

sum 1 1.5 3

$Mean=Σx∗P(x)=1.5$

$Variance = \Sigma x^2*P(x) - Mean^2 = 3 - 1.5^2 = 0.75$

Standard deviation = (0.75)^0.5 = 0.866

There is a difficulty that a random variable takes on integer values, but the mean and the standard deviations are real numbers, they can be rounded to adjust them.