Mathematics, 23.07.2020 03:01 logan12345677885675

Calculate the expected value, the variance, and the standard deviation of the given random variable X. (Round all answers to two decimal places.) X is the number of red marbles that Suzan has in her hand after she selects four marbles from a bag containing four red marbles and two green ones.

Answers: 2

Show answers

Answers

Answer from: nayelimoormann

Using the hypergeometric distribution, it is found that:

The expected value is of 2.67.The variance is of 0.356.The standard deviation is of 0.596.

The marbles are chosen without replacement, hence, the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

In this problem:

6 marbles, hence N = 6

4 red marbles, hence k = 4

She selects 4 marbles, hence n = 4

The expected value is:

$E(X) = \frac{nk}{N}$

Hence:

$E(X) = \frac{4(4)}{6} = 2.67$

The expected value is of 2.67.

The variance is:

$V(X) = \frac{nk(N-k)(N-n)}{N^2(N-1)}$

Hence:

$V(X) = \frac{4(4)(2)(2)}{6^2(6-1)} = 0.356$

The standard deviation is the square root of the variance, hence:

$\sqrt{V(X)} = \sqrt{0.356} = 0.596$

The variance is of 0.356.The standard deviation is of 0.596.

A similar problem is given at link

Answer from: goat561

The answer is below

Step-by-step explanation:

Since they are two green balls, x cannot assume value of 0 and 1. The minimum number of red balls must be two since there are only two green balls and we need to select 4 balls

For x = 2 (select two red balls from 4 red balls and 2 green balls from 2 green balls):

P(x = 2) = $\frac{C(4,2)*C(2,2)}{C(6,2)} =\frac{6}{15}$

For x = 3 (select 3 red balls from 4 red balls and 1 green balls from 2 green balls):

P(x = 3) = $\frac{C(4,3)*C(2,1)}{C(6,2)} =\frac{8}{15}$

For x = 4 (select 4 red balls from 4 red balls and 0 green balls from 2 green balls):

P(x = 4) = $\frac{C(4,4)*C(2,0)}{C(6,2)} =\frac{1}{15}$

Expected value = E(x) = ΣxP(x) = (2×6/15) + (3×8/15) + (4×1/15) = 40/15 = 2.67

Variance = Σx²P(x) - [E(x)]² = (2²×6/15) + (3²×8/15) + (4²×1/15) - (40/15)² = 80/225 = 0.36

Standard deviation = √variance = √0.36 = 0.6

Answer from: Quest

Idon’t know but you’ll figure it out

Answer from: Quest

the answer would be d.

step-by-step explanation:

move all variables to the left side and all constants to the right side

(x−3)^2+(y−1)^2=16

this is the form of a circle. use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

match the values in this circle to those of the standard form. the variable r represents the radius of the circle, h represents the x-offset from the origin, and k represents the y-offset from origin.

r = 4

h = 3

k = 1

the center of the circle is found at ( h , k ) .

center: ( 3 , 1 )

these values represent the important values for graphing and analyzing a circle.

center: ( 3 , 1 ).

radius: 4