M/9+2/3=7/3<br><br> Solve for m.

Calculate the expected value, the variance, and the standard deviation of the given random variable X. (Round all answers to two

Tom [10]

Answer:

E (X) = 1.8

Var (X) = 0.36

σ = 0.6

Step-by-step explanation:

Solution:-

- Denote the random variable X : is the number of red marbles that Suzan has in her hand after she selects three marbles.

- Total sample space (bag) have the following quantity of colored marbles:

Bag : { 3 Red , 2 Green }

- Suzan selects three marbles from the bag. The Event (X) defines the number of red marbles out of 3.

- The total number of outcomes / selections for randomly selecting 3 balls from the bag:

All outcomes = 5 C 3 = 10

- The probability distribution of the random variable X, we will use combinations to determine the required probabilities:

X = 1 red marble:

P ( X = 1 ) : Suzan chooses 1 Red marble from the available 3 red marble and 2 green marbles.

P ( X = 1 ) = [ 3C1*2C2 ] / all outcomes = (3*1) / 10 = 0.3

X = 2 red marble:

P ( X = 2 ) : Suzan chooses 2 Red marble from the available 3 red marble and 1 green marbles.

P ( X = 2 ) = [ 3C2*2C1 ] / all outcomes = (3*2) / 10 = 0.6

X = 3 red marble:

P ( X = 3 ) : Suzan chooses 3 Red marble from the available 3 red marble.

P ( X = 3 ) = [ 3C3] / all outcomes = (1) / 10 = 0.1

- The probability distribution is as follows:

X : 1 2 3

P (X): 0.3 0.6 0.1

- The expected value E(X) for the given random variable X is:

E ( X ) = ∑Xi*P(Xi)

= 1*0.3 + 2*0.6 + 3*0.1

=1.8

- The variance Var(X) for the given random variable X is:

Var ( X ) = ∑Xi^2*P(Xi) - [ E(X) ] ^2

= 1^2*0.3 + 2^2*0.6 + 3^2*0.1 - 1.8^2

= 0.36

- The standard deviation for the given random variable X is:

σ = √Var(X)

σ = √0.36

σ = 0.6

5 0

3 years ago

Omas is making trail mix using granola and walnuts. He can spend a total of $12 on the ingredients. He buys 3 pounds of granola

Serga [27]

Answer:

Omas can buy 1 pound of walnuts.

Step-by-step explanation:

From the information given, you can say that the total cost would be equal to the result of multiplying the price per pound of granola for the number of pounds of granola plus the result of multiplying the price per pound of walnuts for the number of pounds of walnuts, which would be:

Total cost=2x+6y, where

x is the number of pounds of granola

y is the number of pounds of walnuts

Now, you can replace the values on the formula and solve for y:

12=(2*3)+6y

12=6+6y

6=6y

y=1

According to this, the answer is that Omas can buy 1 pound of walnuts.

4 0

2 years ago

Read 2 more answers

Tyler wants to buy a new tub and that cost $312. He has already saved the plan to save $24 per week over the next few weeks whic

laila [671]

Answer:

13 weeks

Step-by-step explanation:

Given that :

Cost of new tub = $312

Planned saving per week = $24

The number of weeks he'll have to save in other to be able to afford the tub can be obtained using the relation :

Number of weeks = cost of new tub / weekly saving

Number of weeks = $312 / $24

Number of weeks = 13 weeks

5 0

2 years ago

Complete the following statement: f(3)=_____

Lesechka [4]

Using this equation, f(3) = 23.

In order to find the value of f(3), we need to take the f(x) equation and put 3 everywhere we see x. Then we follow the order of operations to solve. So, let's start with the original.

f(x) = 2x^2 + 5sqrt(x - 2)

Now place 3 in for each x.

f(3) = 2(3)^2 + 5sqrt(3 - 2)

Now square the 3.

f(3) = 2(9) + 5 sqrt(3 - 2)

Do the subtraction inside of the parenthesis.

f(3) = 2(9) + 5sqrt(1)

Take the square root

f(3) = 2(9) + 5(1)

Multiply.

f(3) = 18 + 5

And add.

f(3) = 23

4 0

3 years ago

Two number cubes are rolled for two separate events:

andrew11 [14]

Answer: $\bold{P(B|A)=\dfrac{P(B\cap A)}{P(A)}=\dfrac{11}{30}}$

<u>Step-by-step explanation:</u>

The probability of Event B given Event A = the intersection of Event A and B divided by the probability of Event A. (see below for the symbols)

$P(B|A)=\dfrac{P(B\cap A)}{P(A)}$

P(A) = (1, 6), (1, 5), (1, 4), (1, 3), (1, 2), (1, 1)

(2, 6), (2, 5), (2, 4), (2, 3), (2, 2), (2, 1)

(3, 6), (3, 5), (3, 4), (3, 3), (3, 2), (3, 1)

(4, 5), (4, 4), (4, 3), (4, 2), (4, 1)

(5, 4), (5, 3), (5, 2), (5, 1)

(6, 3), (6, 2), (6, 1)

= 30

P(B) = (1, 2), (2, 1) sum = 3

(1, 5), (2, 4), (3, 3), (4, 2), (5, 1) sum = 6

(3, 6), (4, 5), (5, 4), (5, 4), (6, 3) sum = 9

(6, 6) sum = 12

= 12

P(A ∩ B) = (1, 2), (2, 1)

(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)

(3, 6), (4, 5), (5, 4), (5, 4), (6, 3)

= 11

7 0

3 years ago

M/9+2/3=7/3 Solve for m.