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3 years ago

A culture of bacteria has an initial population of 7100 bacteria and doubles every 2

Mathematics

1 answer:

Allisa [31]3 years ago

3 0

Answer:

Pt=1285237.2855≈ 1285237

YOUR WELCOME :)

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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

4 years ago

Why does this system of equations have infinitely many solutions?

lapo4ka [179]

Step-by-step explanation:

I would say the one that says after eliminating a variable,the result is x=0

cause the zero can change into any number.

6 0

3 years ago

The opposite of the fraction one third

lozanna [386]

The opposite of the fraction one third would be negative one third. To be opposite, they must have differing signs. One number should be positive and the other number should be negative. It is different from reciprocal. To be a reciprocal, one number should be the flipped fraction, or upside down version, of the other number.

3 0

3 years ago

What is the best way to determine the graph of a situation?

elixir [45]

Answer:

iys answer can be

by drawing

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3 years ago

I need help in area it's hard

Fofino [41]

The area is the length times the width. Find area of shapes by counting unit squares. Some shapes will require combining partial square units to find area.

For example - A rectangle is 5 centimeters long and 4 centimeters wide. What is its area? 

Area = Length * width

The length is 5 centimeters. The width is 4 centimeters. So the area is 5 times 4 square centimeters.

= 20 square centimeters

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3 years ago