Discrete and Continuous Random Variables
1.
Let X be a random number between 0 and 1 produced by a uniform random number
generator. Find the probabilities:
a.)
Sketch a picture of the density curve of the random variable X
b.)
P(0.3
≤
X
≤
0.5)
c.)
P(0.3 < X < 0.5)
d.)
P(0.27
≤
X
≤
1.27)
e.)
P(0.1
≤
X
≤
0.2 or 0.8
≤
X
≤
f.)
P(0.226
≤
X < 0.713)
g)
The probability that X is not in the interval 0.3 to 0.8
h.)
P(X = 0.5)
2.
Nonstandard dice can produce interesting distributions of outcomes. You have two balanced,
six-sided dice. One is a standard die, with faces having 1, 2, 3, 4, 5, and 6 spots. The other die
has three faces with 0 spots and three faces with 6 spots. Create the probability distribution for
the sum of the spots X on the top faces when you roll these two dice.
0.9)

3.
In government data, a household consists of all occupants of a dwelling unit, while a family
consists of two or more persons who live together and are related by blood or marriage. So all
families form households, but some households are not families. Here are the distributions of