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Four balls numbered 1, 2, 3, and 4 are placed in a bowl. After the balls are mixed, one is chosen, its number is noted, then it is replaced. Doing the experiment repeatedly many times, find the variance and standard deviation of the numbers on the balls.​

Respuesta :

Probability is a branch of mathematics that deals with the occurrence of a random event.

Variance is  1.25 and standard deviation is  1.12 .

Since, Four balls numbered 1, 2, 3, and 4 are placed in a bowl

Here, X is random variable and it represents ball with number and P(X) represents probability.

X              1         2          3          4

P(X)         1/4       1/4       1/4        1/4

Mean (μ) = ΣXP(X)

              =  1/4  + 1/2 + 3/4 + 4/4

              = 5/2

Variance = Σ (X^2P(X))  - μ^2

Σ (X^2P(X))  = 1/4 + 4/4 + 9/4 + 16/4

              = 30/4 = 7.5

So, Variance = 7.5 - 6.25 = 1.25

[tex]Deviation = \sqrt{Variance}[/tex]

Standard deviation =  [tex]\sqrt{1.25}[/tex] = 1.12

Learn more:

https://brainly.com/question/475676

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