程序代写代做代考 QBUS6820 Probability quiz

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) ?