QBUS6820 Probability quiz
1. Given this density function:
Which of these options represents the Cumulative Distribution Function?
A.
B.
C.
1
0 1 1/2
0 1 1/2
1
0 1 1/2
0 1 1/2
1
2. Given this density function:
Which of these options represents the Cumulative Distribution Function?
A.
B.
C.
0 1 1/2
1
0 1 1/2
0 1 1/2
1
0 1 1/2
1
3. Given this (discrete) density function:
Which of these options represents the Cumulative Distribution Function?
A.
B.
C.
0 1 1/4 3/4
0 1 1/2
1
0 1 1/2
1
0 1 1/2
1
4. Given this density function:
Which of these options represents the Cumulative Distribution Function?
A.
B.
C.
0 1 1/2
0 1 1/2
1
0 1 1/2
1
0 1 1/2
1
5. A fair dice is thrown. The event A is that the number is odd (i.e. 1, 3 or 5). Find an event B such that
Pr([ ) is not equal to Pr() + Pr()
6. Using the same definition of the event A as in question 5, let C be the event that the dice shows 4,
5 or 6. What is Pr(A j C) (i.e. what is the probability of A given that C occurs)?
7. Let F be the cumulative distribution function and f the density function for the uniform distribution
on (0, 1) (for which every value between 0 and 1 is equally likely). What is F(0.5) and what is
f(0.5)?
8. A random variable takes the value 1 with probability 2/3 and the value 4 with probability 1/3. What
is the mean and variance of this random variable?
9. A triangular random variable has f(x) = x for x 2 [0,1] and f(x) = 2 – x for x 2 [1, 2]. What is
F(1.5) ?