Question

below is pmf of Z:

 Z P(Z) -3 1/16 -2 1/8 -1 3/16 0 1/4 1 3/16 2 1/8 3 1/16

a)E(Z) =ΣzP(z) = 0

b) P(Z=-1 |Z<1) =P(Z=-1)/P(Z<1) =(3/16)/(5/8)=3/10 =0.3

c) P(Z=2 in fourth attempt) =P(first 3 failures and 4th failure) =(1-1/8)^3*(1/8)=343/4096

d) from binomial distribution: P(4 times out of 10) =C(10,4)*(1/4)4*(3/4)6 =0.1460

#### Earn Coins

Coins can be redeemed for fabulous gifts.

Similar Homework Help Questions
• ### Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented...

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 0 to 3. 1. (2.5 points) Find E(Z). 2. (2.5 points) Find P(Z = 21Z >1). 3. (2.5 points) What is the probability that you have to play the game 6 times before you roll...

• ### Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented...

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 2-8. 1.(2.5 points) Find E(Z). 2. (2.5 points) Find P(Z = 71Z > 5). 3.(2.5 points) What is the probability that you have to play the game 4 times before you roll Z=7? 4. (2.5...

• ### Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented...

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 2-8. 1.(2.5 points) Find E(Z). 2. (2.5 points) Find P(Z = 71Z > 5). 3.(2.5 points) What is the probability that you have to play the game 4 times before you roll Z=7? 4. (2.5...

• ### Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented...

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. 1. (2.5 points) Find E(Z). 2. (2.5 points) Find P(Z =-1|Z < 1). 3. (2.5 points) What is the probability that you have to play the game 3 times before you roll...

• ### Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented...

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 0 to 3. 1. Find E(Z). 2. Find P(Z = 1|Z <3). 3. What is the probability that you have to play the game 4 times before you roll Z=3? 4. What is the probability...

• ### Roll two fair four-sided dice. Let X and Y be the die scores from the 1st...

Roll two fair four-sided dice. Let X and Y be the die scores from the 1st die and the 2nd die, respectively, and define a random variable Z = X − Y (a) Find the pmf of Z. (b) Draw the histogram of the pmf of Z. (c) Find P{Z < 0}. (d) Are the events {Z < 0} and {Z is odd} independent? Why?

• ### dice is unbiased. Throws independent. Step 1. You roll a six-sided die. Let X be the...

dice is unbiased. Throws independent. Step 1. You roll a six-sided die. Let X be the (random) number that you obtain. Step 2. You roll X six-sided dice. Let Y be the total number (sum) that you obtain from these X dice. Find E[Y] rounded to nearest .xx.

• ### Step 1. You roll a six-sided die. Let X be the (random) number that you obtain....

Step 1. You roll a six-sided die. Let X be the (random) number that you obtain. Step 2. You roll X six-sided dice. Let Y be the total number (sum) that you obtain from these X dice. Find E[Y], rounded to nearest .XX.

• ### There exists 3-sided dice. Such a die, when you roll it, will show 1, 2, or...

There exists 3-sided dice. Such a die, when you roll it, will show 1, 2, or 3 with equal probability. The experiment is to roll 3 such dice. Random variable T is the total of all 3 dice. t P(T=t) 3 4 5 6 7 8 9

• ### 2. (25 points) Sekora International Casino (SIC) is launching a new game making use of fair 6-sided dice . In phase 1, roll two 6-sided dice and compute the difference between the rolls. Call thi...

2. (25 points) Sekora International Casino (SIC) is launching a new game making use of fair 6-sided dice . In phase 1, roll two 6-sided dice and compute the difference between the rolls. Call this difference . In phase 2, roll r dice, and add up the total of the rolls. This is the payout in dollars of the game. (with the numbers 1-6 on the sides). The game proceeds in two phases as follows: (a) (5 points) In the...