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Let x denote the sum of two distinct numbers selected randomly from the set of numbers StartSet 1 comma 2 comma 3 comma 4 comma 5 EndSet . {1, 2, 3, 4, 5}. Construct the probability distribution for the random variable x.

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thaovtp1407

Answer:

Step-by-step explanation:

Given:

The set of numbers {1, 2, 3, 4, 5}

Affter that, we find the sum um of two distinct numbers selected randomly from the set above;

  • 1+2 =3
  • 1+3=4
  • 1+4=5
  • 1+5=6
  • 2+3=5
  • 2+4=6
  • 2+5=7
  • 3+4=7
  • 3+5=8
  • 4+5 = 9

Therefore, we have the following number: 3,4,5,6,5,6,7,7,8,9

so we have x = {3,4,5,6,5,6,7,7,8,9 }

now we find P(x) of each number, we have n(S) = 10

x  3 4 5 6 7 8 9

P(x)  1/10 1/10 1/10 2/10 2/10 2/10 1/10

Hope it will find you well.

MrRoyal

The probability distribution of a set gives the probabilities of possible outcomes of the set

The set of numbers is given as:

[tex]\mathbf{Set = \{1, 2, 3, 4, 5\}}[/tex]

Add two distinct numbers of the set.

The sum is as follows

[tex]\mathbf{1+2 =3}[/tex]

[tex]\mathbf{1+3=4}[/tex]

[tex]\mathbf{1+4=5}[/tex]

[tex]\mathbf{1+5=6}[/tex]

[tex]\mathbf{2+3=5}[/tex]

[tex]\mathbf{2+4=6}[/tex]

[tex]\mathbf{2+5=7}[/tex]

[tex]\mathbf{3+4=7}[/tex]

[tex]\mathbf{3+5=8}[/tex]

[tex]\mathbf{4+5 = 9}[/tex]

The sum of the distinct numbers are:

[tex]\mathbf{Sum = \{3,4,5,6,5,6,7,7,8,9\}}[/tex]

Calculate the probability of each number in the sum set i.e. 3, 4, 5, 6, 7, 8 and 9

[tex]\mathbf{P(3) = P(4) = P(5)= P(9)= \frac{1}{10} = 0.10}[/tex]

[tex]\mathbf{P(6) = P(7) = P(8)= \frac{2}{10} = 0.20}[/tex]

So, the probability distribution for the random variable is:

x   - - P(x)

3 -- 0.10

4 -- 0.10

5 -- 0.10

6 -- 0.20

7 -- 0.20

8 -- 0.20

9 -- 0.10

Read more about probability distributions at:

https://brainly.com/question/795909

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