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grigory [225]
3 years ago
15

g Consider the experiment of a single roll of an honest die and a single toss of 3 fair coins. Let X be the value on the die and

let Y be the number of heads obtained on the coins. Find the joint probability function of X and Y
Mathematics
1 answer:
klemol [59]3 years ago
4 0

Answer:

The probability function of X and Y is

P(X = k, Y = 0)  = 1/48\\P(X = k, Y = 1) = 1/16\\P(X = k, Y = 2) = 1/16\\P(X = k, Y = 3) = 1/48

With k in {1,2,3,4,5,6}

Step-by-step explanation:

We can naturally assume that X and Y are independent. Because of that, P(X=a, Y=b) = P(X=a) * P(Y=b) for any a, b.

Note that, since the die is honest, then P(X=k) = 1/6 for any k in {1,2,3,4,5,6}. We can conclude as a consequence that P(X=k, Y=l) = P(Y=l)/6 for any k in {1,2,3,4,5,6}.

Y has a binomial distribution, with parameters n = 3, p = 1/2. Y has range {0,1,2,3}. Lets compute the probability mass function of Y:

P_Y(0) = {3 \choose 0} * 0.5^3 = 1/8

P_Y(1) = {3 \choose 1} * 0.5* 0.5^2 = 3/8

P_Y(2) = {3 \choose 2} * 0.5^2*0.5 = 3/8

P_Y(3) = {3 \choose 3} * 0.5^3 = 1/8

Thus, we can conclude that the joint probability function is given by the following formula

P(X = k, Y = 0) = 1/8 * 1/6 = 1/48\\P(X = k, Y = 1) = 3/8 * 1/6 = 1/16\\P(X = k, Y = 2) = 3/8 * 1/6 = 1/16\\P(X = k, Y = 3) = 1/8 * 1/6 = 1/48

For any k in {0,1,2,3,4,5,6}

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faltersainse [42]
The answer is 11040 square yards because you have to convert the answer into yards so yeah
5 0
3 years ago
Point S is on line segment R T ‾ RT . Given R S = 4 x − 10 , RS=4x−10, S T = 2 x − 10 , ST=2x−10, and R T = 4 x − 4 , RT=4x−4, d
mylen [45]

Question not well presented

Point S is on line segment RT . Given RS = 4x − 10, ST=2x−10, and RT=4x−4, determine the numerical length of RS

Answer:

The numerical length of RS is 22

Step-by-step explanation:

Given that

RS = 4x − 10

ST=2x−10

RT=4x−4

From the question above:

Point S lies on |RT|

So, RT = RS + ST

Substitute values for each in the above equation to solve for x

4x - 4 = 4x - 10 + 2x - 10 --- collect like terms

4x - 4 = 4x + 2x - 10 - 10

4x - 4 = 6x - 20--- collect like terms

6x - 4x = 20 - 4

2x = 16 --- divide through by 2

2x/2 = 16/2

x = 8

Since, RS = 4x − 10

RS = 4*8 - 10

RS = 32 - 10

RS = 22

Hence, the numerical length of RS is calculated as 22

8 0
3 years ago
Plz help meeeeeeeeeee
PSYCHO15rus [73]

Answer:

Please check the explanation.

Step-by-step explanation:

We know the equation

y = kx

k = y/x

where k is the proportionality constant

so,

First ratio can be calculated as

Miles = 45

Hours = 3/4

The ratio = 45 / (3/4)

                = (45 × 4) / 3

                = 180/3

                = 60

Thus, the proportionality constant = 60

Thus, the remaining ratios can be calculated as:

The Pair (135, Hours)

135/Hours = 60

Hours = 135 / 60

           = 27/12

           = 9/4

           = 2.25

Thus, the pair is (135, 2.25)

The Pair (Miles, 3)

Miles/3 = 60

Miles = 60×3

         = 180

The Pair (90, Hours)

90/Hours = 60

Hours = 90 / 60

          = 3/2

          = 1.5

Thus, the complete table:

Miles           45           135           180             90

Hours           3/4          9/4           3                 3/2

Verification:

Miles / Hour =  45/(3/4) = 60

Miles / Hour = 135 / 2.25 =  60

Miles / Hour = 180 / 3 = 60

Miles / Hour  = 90 / 1.5 =  60      

8 0
2 years ago
The coaches at Xavier Elementary School bought cases of sports drinks for a field day. They bought 76 cases of drinks. Each case
solong [7]

Answer:

608

Step-by-step explanation:

There are a total of 1,824 drinks since there were 76 cases at 24 drinks a piece. This creates a total number of 24*76 = 1824.

If each student receives 3 then 1824/3 = 608. There were 608 students.

7 0
3 years ago
Which of the following is an example of an irrational number
MAVERICK [17]

Answer:

D.

D is the answer because if you complete the problem it does not equal out

8 0
3 years ago
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