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4 years ago

What does the PErron-Frobenius Theorem say, and why is it useful?

Mathematics

1 answer:

Alex787 [66]4 years ago

5 0

Answer:

Perron–Frobenius theorem for irreducible matrices. Let A be an irreducible non-negative n × n matrix with period h and spectral radius ρ(A) = r. Then the following statements hold. The number r is a positive real number and it is an eigenvalue of the matrix A, called the Perron–Frobenius eigenvalue.

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A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 50% of this population prefers t

NeX [460]

Answer:

0.09

Step-by-step explanation:

Given that 50% of this population prefers the color green.

Let p the probability that one person selected from the population prefer the green color of the car. So,

p=0.05

There is only two chance, any person either prefer the green color or not, assuming this holds true for every person, so the mentioned population can be assumed as Bernoulli's population.

By using Bernoulli's theorem, the probability of exactly r success of n randomly selected from the Bernoulli's population is

$P(r)=\binom{n}{r}p^{r}{(1-p)}^{n-r}\cdots(i)$

Here, 15 buyers are randomly selected, so, n= 15 and

$r= \frac1 3 \times 15=5$

So, by using equation (i), the probability that exactly 5 buyers would prefer green out of 15 randomly selected buyers is

$P(r=5)=\binom{15}{5}(0.5)^{5}{(1-0.5)}^{15-5}$

$=\binom{15}{5}(0.5)^{5}{0.5}^{10}$

$=\binom{15}{5}(0.5)^{15}$

=0.0916

Hence, the probability that exactly 5 buyers would prefer green out of 15 randomly selected buyers is 0.09.

3 0

3 years ago

PLEASE help (desperate) :(

mars1129 [50]

Answer:

$4= \sqrt{16} \\1.5 = \sqrt{2.25}\\8 = 6^{2} /9*2\\1 = \frac{12 - 2}{6 + 4}\\5 = \sqrt{16 + 9} \\9 = 63/3^{2} +|2|$

6 0

3 years ago

Jordan spent 22% of his time doing math homework. If hw spent 11 minutes on his math homework. How many minutes did he spend on

devlian [24]

Answer:

The total minutes he spend on his homework are 50 minutes.

Step-by-step explanation:

<em>It is given that Jordan spent 22% of his time for homework on maths.</em>

<em>It is also given that he spent 11 minutes of time on maths homework.</em>

The above two statements are equal.

Let the total time for homework be "x".

Thus, the equation can be written as,

$(\frac{22}{100})(x) = 11$

$x = (\frac{100}{22})(11) = 50 minutes$

Thus the total minutes he spend on his homework are 50 minutes.

3 0

3 years ago

Assume that all (525)poker hands are equally likely. What is the probability that you will be dealt:

AlekseyPX

Answer:

There is 1.98% of probability of being dealt a flush in 5-card Poker

Step-by-step explanation:

To know the probability of a flush being dealt, we can calculate the number of cases when that happens and divide it by the total number of cases of poker hands that exist, naming A the event of a flush.

We will use combinations (nCr button on a calculator) to count the number of cases, because we don't care about the order (it is the same to be dealt a 2, 4, 6, 7 and 8 of hearts than the opposite order), being a flush the event when we take 5 cards out of 13 of the same suit, times 1 out of 4 possible suits and the total number of cases is taking 5 random cards out of 52.

$P_{A} =\frac{Cases Of Flush}{Hands} =\frac{\left(\begin{array}{ccc}13\\5\end{array}\right)*\left(\begin{array}{ccc}4\\1\end{array}\right)}{\left(\begin{array}{ccc}52\\5\end{array}\right)} =\frac{5148}{2598960}=0,00198\\$

That means there is about a 2% of probability of being dealt a flush.

In other words, of every 16660 plays, 33 will be, on average, a flush

6 0

3 years ago

La expecion del volumen

Free_Kalibri [48]

Answer:

no hay imagen lo siento

Step-by-step explanation:

3 0

3 years ago