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faithcalhoun
08.04.2021 •
Mathematics
Daniela is decorating her room. She has 14 shades of paint, 6 styles of furniture, and 11 flooring options to choose from. How many different ways can she decorate the room?
1- 2,706 different ways.
2-660 different ways.
3-330 different ways.
4-924 different ways
Solved
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Ответ:
A part of the question is missing and it says;
b) Calculate the variance of the amount you win.
A) Expected value of Pay out;
(E(Y)) = - 0.11
B) Variance of the amount won; Var(Y) = 0.9879
Step-by-step explanation:
A) From the question, we have;
X ∈ {0,1,2} and by the nature of the question, X has a hypergeometric distribution as;
P(X =i) = [(5,i) (5, 2 - i)] / (10,2)
Furthermore, when we consider the random variable Y that marks the amount of money that we win, we'll get a function of X as;
Y = 1X [x∈{0,2}] - [1X(x=1)]
If we now use the linearity of expectation, we'll get;
E(Y) = E [X(x∈{0,2}) ] - [E(X(x=1))]
= P(X = 0) + P(X = 2) - P(X = 1)
For 2 balls with probability of a win, P = (possible outcome) /(total outcome) =
{(2C1) (5C2)}/(10C2) = (2 x 10)/45 = 20/45
While, for probability of no win;
P = 1 - (20/25) = 25/25
So, E(Y) =20/45 - 25/45 = - 5/45 =
- 0.11
B) Now let's calculate for the variance;
Var(Y) = E(Y(^2)) - E(Y)^(2)
Now, from question a, using the equation of Y, we can say;
(Y)^(2) = (1^2)X [x∈{0,2}] - [(1^2)X(x=1)]
And so;
E(Y^(2)) = P(X = 0) + P(X = 2) + P(X = 1) = (1^2)(20/45) + (-1^2)(25/45) = 45/45 = 1
So, Var(Y) = 1 - (-0.11)^2 = 0.9879