Question

Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented by random variable X and those of th

0 0
Add a comment Improve this question Transcribed image text
Answer #1

Answer:

Given that,

Suppose you roll two 4 sided dice.

Let the probabilities of the first die be represented by random variable X and those of the second die be represented by random variable Y Let random variable Z be (X-Y).

The range of Z will be from -3 to 3.

The values of Z are computed for different X and Y as:

Y=1 Y=2 Y=3 Y=4
X=1 Z=0 Z=-1 Z=-2 Z=-3
X=2 Z=1 Z=0 Z=-1 Z=-2
X=3 Z=2 Z=1 Z=0 Z=-1
X=4 Z=3 Z=2 Z=1 Z=0

P(Z = -3) = 1/16
P(Z = -2) = 2/16
P(Z = -1) = 3/16
P(Z = 0) = 4/16
P(Z = 1) = 3/16
P(Z = 2) = 2/16
P(Z = 3) = 1/16

(1).

Find E(Z):

The expected value here is computed as:

E(Z) = (3/16)(-1 + 1) + (2/16)(-2 + 2) + (1/16)(3 - 3) + 0(4/16) = 0

Therefore E(Z) = 0

(2).

Find P(Z =-1|Z < 1):

P(Z = -1 | Z < 1) is computed using bayes theorem as:

P(Z = -1) / P(Z < 1)

= 1/10

= 0.1

Therefore 0.1 is the required probability here.

(3).

P(Z = 2) = 2/16

Probability that the game has to be played 4 times before we get z = 2 is computed here as:

= (14/16)^3(2/16)

= 0.0837

Therefore 0.0837 is the required probability here.

(4).

P(Z = 0) = 4/16

The required probability here is computed as:

\small = \binom{10}{4}(4/16)^4(12/16)^6

=210(0.039)(0.17798)

=1.4577

Add a comment
Know the answer?
Add Answer to:
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT