Which of the following rational numbers is equal to 4.7 with a line on top of 7 ?

. Let X and Y be random variables of possible percent returns (0%, 10%,

bazaltina [42]

(a) The marginal distribution of X is

Pr(X = x) = ∑ Pr(X = x, Y = y)

… = 0.0625 + 0.0625 + 0.0625 + 0.0625

… = 0.25

That is, the first equality follows from the law of total probability, with the sum taken over y from {0, 5, 10, 15}. Each probability Pr(X = x, Y = y) is given in the table to be 0.0625.

Similarly, the marginal distribution of Y is

Pr(Y = y) = 0.25

(b) Yes, they're independent because

Pr(X = x, Y = y) = 0.0625,

and

Pr(X = x) Pr(Y = y) = 0.25 • 0.25 = 0.0625.

(c) The mean of X is

E[X] = ∑ x Pr(X = x)

… = 0.25 ∑ x

… = 0.25 (0 + 5 + 10 + 15)

… = 7.5

and you would find the same mean for Y,

E[Y] = 7.5

The variance of X is

V[X] = E[X^2] - E[X]^2

… = (∑ x^2 Pr(X = x)) - 7.5^2

… = 0.25 (∑ x^2) - 56.25

… = 0.25 (0^2 + 5^2 + 10^2 + 15^2) - 56.25

… = 31.25

and similarly,

V[Y] = 31.25

(each sum is taken with x and y from {0, 5, 10, 15})

7 0

3 years ago

Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 19. Use the empirical rule

zvonat [6]

Answer: About 99.7% IQ scores falls within 43 and 157.

Step-by-step explanation:

According to the empirical rule , if a data follows normal distribution then about 99.7% of the population lies with in three standard deviations from mean.

Given: IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 19.

Since , the graph of normal distribution is bell-shaped , it mean that IQ scores follow normal distribution.

Then, About 99.7% IQ scores falls within Mean ± 3 (Standard deviation).

i.e. About 99.7% IQ scores falls within 100± 3(19).

i.e. About 99.7% IQ scores falls within 100- 57 and 100+57.

i.e. About 99.7% IQ scores falls within 43 and 157.

Therefore , by empirical rule

About 99.7% IQ scores falls within 43 and 157.

3 0

3 years ago

I need help! asap please

nasty-shy [4]

Answer:

-1/1

Step-by-step explanation:

it's negative 1 over one because the graph is constantly going down but still to the right side and the line is touching every corner of the boxes

6 0

2 years ago

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Can y’all help me with it pls

Marta_Voda [28]

Answer:

1. D

2. C

3. C, A F

Step-by-step explanation:

4 0

2 years ago

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Karen karlin bought some large frames for $15 each and some small frames for $8 each at a closeout sale. if she bought 22 frames

BaLLatris [955]

small frames ($8): s

large frames ($15): L

Cost: 8s + 15L = 239 ⇒ 1(8s + 15L = 239) ⇒ 8s + 15L = 239

Quantity: s + L = 22 ⇒ -8( s + L = 22) ⇒ -8s -8 L = -176

7L = 63

L = 9

Quantity: s + L = 22 ⇒ s + (9) = 22 ⇒ s = 13

Answer: 13 small frames, 9 Large frames

7 0

3 years ago

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