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.

Using the hypergeometric distribution, it is found that:

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

Hypergeometric distribution:

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:

The expected value is:

Hence:

The expected value is of 2.67.

The variance is:

Hence:

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

A similar problem is given at link

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) =

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

P(x = 3) =

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

P(x = 4) =

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

step-by-step explanation:

the first 5 right here the next 5 i will upload as separate question

this doesn't make sense lol