Question

In: Math

Suppose we would roll two standard 6-sided dice. (a) Compute the expected value of the sum...

Suppose we would roll two standard 6-sided dice.

(a) Compute the expected value of the sum of the rolls.

(b) Compute the variance of the sum of the rolls.

(c) If X represents the maximum value that appears in the two rolls, what is the expected value of X? What’s the probability of sum = 7?

Solutions

Expert Solution

The probability distribution

So then we compute the expected value, using

E(X)= ∑x(P(X)=x)

         =2⋅1/36+3⋅2/36+4⋅3/36+5⋅4/36
             +6⋅5/36+7⋅6/36+8⋅5/36+9⋅4/36
             +10⋅3/36+11⋅2/36+12⋅1/36

         =(2+6+12+20+30+42+40+36+30+22+12)/36

         =252/36

         =7

Variance = sumation of (X- mean)2*f(x)

=

So then we compute the expected value, using

E(X)=∑x(P(X)=x)

         =(2-7)2⋅1/36+(3-7)2⋅2/36+(4-7)2⋅3/36+(5-7)2⋅4/36
             +(6-7)2⋅5/36+(7-7)2⋅6/36+(8-7)2⋅5/36+(9-7)2⋅4/36
             +(10-7)2⋅3/36+(11-7)⋅2/36+(12-7)2⋅1/36

         =35/6

Probability of x=7 is 6/36 = 1/6


Related Solutions

Suppose you roll two 6 sided dice, letting X be the sum of the numbers shown...
Suppose you roll two 6 sided dice, letting X be the sum of the numbers shown on the dice and Y be the number of dice that show an odd number. a) Find the joint pmf of <X,Y> b) Find the marginals pmf's for both variables. c) Are X and Y independent?
Suppose you roll two 6 sided dice, letting X be the sum of the numbers shown...
Suppose you roll two 6 sided dice, letting X be the sum of the numbers shown on the dice and Y be the number of dice that show an odd number. a) Find the joint pmf of <X,Y> b) Find the marginals pmf's for both variables. c) Are X and Y independent?
Suppose you roll two 6-sided dice, letting X be the sum of the numbers shown on...
Suppose you roll two 6-sided dice, letting X be the sum of the numbers shown on the dice and Y be the number of dice that show an odd number. a) Find the joint pmf of <X,Y> b) Find the maringals pmf's for both variables. c) Are X and Y independent?
1a) Let an experiment consist of rolling three standard 6-sided dice. i) Compute the expected value...
1a) Let an experiment consist of rolling three standard 6-sided dice. i) Compute the expected value of the sum of the rolls. ii) Compute the variance of the sum of the rolls. iii) If X represents the maximum value that appears in the two rolls, what is the expected value of X? 1b) Consider an experiment where a fair die is rolled repeatedly until the first time a 3 is observed.    i) What is the sample space for this...
Suppose you roll, two 6-sided dice (refer back to the sample space in the sample space...
Suppose you roll, two 6-sided dice (refer back to the sample space in the sample space notes). Write any probability as a decimal to three place values and the odds using a colon. Determine the following: a. the probability that you roll a sum of seven (7) is . b. The odds for rolling a sum of four (4) is . c. The odds against the numbers on both dice being the same is .
You roll two 6-sided dice numbered 1 through 6. Let A be the event that the...
You roll two 6-sided dice numbered 1 through 6. Let A be the event that the first die shows the number 3, let B be the event that the second die shows a 5, and let E be the event that the sum of the two numbers showing is even. Compute P(A)and P(B)and then compute P(AlB). What does this tell you about events A and B?Hint: Remember that the sample space has 36 outcomes! Compute P(ElA)and compute P(E). What does...
A player pays $ 13 to roll three six-sided balanced dice. If the sum of the...
A player pays $ 13 to roll three six-sided balanced dice. If the sum of the 3 dice is less than 13, then the player will receive a prize of $ 70. Otherwise, you lose the $13. a. Find the expected value of profit.
DESCRIPTION Complete the given program to simulate the roll of two 6-sided dice and count the...
DESCRIPTION Complete the given program to simulate the roll of two 6-sided dice and count the number of rolls of each possible roll value (2 to 12). The number of rolls will be input by the user. Count the rolls of each type and then "draw" a histogram by printing a "*" for each roll of each type. The shape of the histogram will follow the "probability distribution" for large numbers of rolls, i.e., it will show more rolls for...
17#13 Suppose we roll a fair six-sided die and sum the values obtained on each roll,...
17#13 Suppose we roll a fair six-sided die and sum the values obtained on each roll, stopping once our sum exceeds 289. Approximate the probability that at least 76 rolls are needed to get this sum.
You roll two fair dice. Let A be the event that the sum of the dice...
You roll two fair dice. Let A be the event that the sum of the dice is an even number. Let B be the event that the two results are different. (a) Given B has occurred, what is the probability A has also occurred? (b) Given A has occurred, what is the probability B has also occurred? (c) What is the probability of getting a sum of 9? (d) Given that the sum of the pair of dice is 9...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT