Mathematics, 26.10.2019 02:43 Esmer1030

Two dice are rolled. let the random variable x denote the number that falls uppermost on the first die and let y denote the number that falls uppermost on the second die.
(a) find the probability distributions of x and y.
(b) find the probability distribution of x + y.

Answers: 1

Show answers

Answers

Answer from: apalacios3503

Step-by-step explanation:

a) Lets start by giving the

The probability distribution of X is:

$P(X=x)=\frac{1}{6}$

For every x = 1, 2, 3, 4, 5, 6

Same for Y:

$P(Y=y)=\frac{1}{6}$

For every y = 1, 2, 3, 4, 5, 6

This is because each variable has 6 possibilities which are equiprobable. In other words, every number (1 to 6) has the same probability of falling uppermost on each dice.

Now if the question refers to a joint probability distribution, then we have a joint random viariable (X,Y). This probability is given by:

$P[(X,Y)=(x,y)] = \frac{1}{36}$

For every x = 1, 2, 3, 4, 5, 6 and y = 1, 2, 3, 4, 5, 6

The reason for this is that the combination of the result of both dices produces 36 equiprobable possibilities.

b) For the probability distribution of the sum of the variables we may define:

Z=X+Y

The for the random variable Z the next results are possible:

Z P(Z)

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

This is our probability distribution for the sum of X+Y. Now to understand the results lets see some examples:

For z = 2 (x=1 and y=1) we obtain the probability $P(Z=2)=\frac{1}{36}$ , this is because we have 1 possibility to obtain (1,1) among 36 possibilities.

For z = 4 that is for (x=1, y=3) and (x=2, y=2) and (x=3, y=1) we obtain $P(Z=4)=\frac{3}{36}$ this is because we have 3 possibilities to obtain any of the combinations mentioned among 36 possibilities.

For z = 10 that is for (x=4, y=6) and (x=5, y=5) and (x=6, y=6) we obtain $P(Z=4)=\frac{3}{36}$ because we have 3 possibilities to obtain any of the combinations mentioned among 36 possibilities.

Answer from: Quest

What are the options for plato

Answer from: Quest

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.

In circle a, bae dae. what is the value of x?

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 15:10, shamiya15

Polygons efgh and e′f′g′h′ are shown on the coordinate grid: what set of transformations is performed on efgh to form e′f′g′h′? a. a translation 1 unit to the left followed by a 90-degree counterclockwise rotation about the origin b. a translation 1 unit to the right followed by a 90-degree counterclockwise rotation about the origin c. a 90-degree clockwise rotation about the origin followed by a translation 2 units to the right d. a 90-degree clockwise rotation about the origin followed by a translation 2 units to the left

Answers: 1

continue

Mathematics, 21.06.2019 17:30, taylor5384

At a sale this week, a desk is being sold for $213. this is a 29% discount from the original price. what is the original price?

Answers: 1

continue

Mathematics, 21.06.2019 22:10, KekePonds1021

Which equation is y = -6x2 + 3x + 2 rewritten in vertex form?

Answers: 1

continue

Mathematics, 21.06.2019 23:00, stodd9503

Frank has a devised a formula for his catering business that calculates the number of meatballs he needs to prepare. the formula is m=4a+2c, where c=number of children; m=number of meatballs; a=number of adults. how many meatballs are required for a party of 10 adults and 5 children?

Answers: 1

continue

You know the right answer?

Two dice are rolled. let the random variable x denote the number that falls uppermost on the first d...