Plzzz Solve these 7 Questions ASAP !! PLZZZZZZZZZZZ IT'S A REQUEST !!!

Let X1, . . . ,Xn ∈ R be independent random variables with a common CDF F0. Let Fn be their ECDF and let F be any CDF. If F = Fn

Georgia [21]

Answer:

See the proof below.

Step-by-step explanation:

For this case we need to proof that: Let $X_1, X_2, ...X_n \in R$ be independent random variables with a common CDF $F_0$ . Let $F_n$ be their ECDF and let F any CDF. If $F \neq F_n$ then $L(F)$

Proof

Let $z_a$ different values in the set { $X_1,X_2,...,X_n}$ } and we can assume that $n_j \geq 1$ represent the number of $X_i$ that are equal to $z_j$ .

We can define $p_j = F(z_j) +F(z_j-)$ and assuming the probability $\hat p_j = \frac{n_j}{n}$ .

For the case when $p_j =0$ for any $j=1,....,m$ then we have that the $L(F) =0< L(F_n)$

And for the case when all $p_j >0$ and for at least one $p_j \neq \hat p_j$ we know that $log(x) \leq x-1$ for all the possible values $x>0$ . So then we can define the following ratio like this:

$log (\frac{L(F)}{L(F_n)}) = \sum_{j=1}^m n_j log (\frac{p_j}{\hat p_j})$

$log (\frac{L(F)}{L(F_n)}) = n \sum_{j=1}^m \hat p_j log(\frac{p_j}{\hat p_j})$

$log (\frac{L(F)}{L(F_n)}) < n\sum_{j=1}^m \hat p_j (\frac{p_j}{\hat p_j} -1)$

So then we have that:

$log (\frac{L(F)}{L(F_n)}) \leq 0$

And the log for a number is 0 or negative when the number is between 0 and 1, so then on this case we can ensure that $L(F) \leq L(F_n)$

And with that we complete the proof.

8 0

3 years ago

Write the slope-intercept form equation of the line that passes through (1,-1) and (2, 2).

mixer [17]

Answer:

The answer to your question is y= 3x - 4.

Step-by-step explanation:

Plot the points (1,-1) and (2,2) and get your slope, in the case of slope-intercept form "m" using the rise/run method. You rise 3 units and run one unit to the right to get from (1,-1) to (2,2), so your slope is 3/1 or just simply 3. -4 is your y-intercept, or "b", because if you plot the two aforementioned points (1,-1) and (2,2) and make a line with them, your line meets the y-axis at the point (0, -4). Hope this helps!

4 0

3 years ago

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Nonamiya [84]

Answer:

black = 0.28

white = 0.22

pink = 0.24

blue = 0.26

Step-by-step explanation:

Jason and his friend spun the spinner 100 times total. So for each time landed on a color, it can be counted as one percentage (for example, black had a 28% frequency). To transfer percentages to decimal form, simply bring the decimal point over by two spaces (28 becomes 0.28, something like 4 would become 0.04). Hope this helps! Feel free to ask any questions!

3 0

3 years ago

Please help! Need answer to number 4

alekssr [168]

Answer: H, 1/21

Step-by-step explanation:

7 letters in October

1 b / 7 letters

2 o / 6 letters

1/7 * 2/6 = 2/42 = 1 / 21

5 0

3 years ago

The inhabitants of the island of jumble use the standard kobish alphabet ($20$ letters, a through t). each word in their languag

rjkz [21]

We know that

1. The number of all 4-letter words written using the alphabet of 20 symbols (from A to T) is
20^4=160,000

2. The number of all 4-letter words written using the alphabet of 19 symbols (from B to T) is
19^4=130,321

3. The difference represents exactly the number of all words of the inhabitants of the island of Jumble
difference=(160,000-130,321)= 29679.

the answer is
29679

7 0

3 years ago