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bazaltina [42]
2 years ago
10

For each given p, let Z have a binomial distribution with parameters p and N. Suppose that N is itself binomially distributed wi

th parameters q and M. For- mulate Z as a random sum and show that Z has a binomial distribution with parameters pq and M.
Mathematics
1 answer:
8090 [49]2 years ago
7 0

Explanation:

Lets interpret Z with M trials. First we have M trials, each trial can be a success or not. The number of success is called N. Each trial that is a success becomes a trial, and if it is a success it becomes a success for Z. Thus, in order for a trial to be successful, it needs first to be successful for the random variable N (and it is with probability q), and given that, it should be a success among the N trials of the original definition of Z (with probability p).

This gives us that each trial has probability pq of being successful. Note that this probability is pq independently of the results of the other trials, because the results of the trials of both N and the original definition of Z are independent. This shows us that Z is the total amount of success within M independent trials of an experiment with pq probability of success in each one. Therefore, Z has Binomial distribution with parameters pq and M.

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Two planes start from the same point and fly in opposite directions. The first plane is flying 60 mph slower than the second pla
Naddik [55]

Answer:

The first plane is moving at 295 mph and the second plane is moving at 355mph.

Step-by-step explanation:

In order to find the speed of each plane we first need to know the relative speed between them, since they are flying in oposite directions their relative speed is the sum of their individual speeds. In this case the speed of the first plane will be "x" and the second plane will be "y". So we have:

x = y - 60

relative speed = x + y = (y - 60) + y = 2*y - 60

We can now apply the formula for average speed in order to solve for "y", we have:

average speed = distance/time

average speed = 1625/2.5 = 650 mph

In this case the average speed is equal to their relative speed, so we have:

2*y - 60 = 650

2*y = 650 + 60

2*y = 710

y = 710/2 = 355 mph

We can now solve for "x", we have:

x = 355 - 60 = 295 mph

The first plane is moving at 295 mph and the second plane is moving at 355mph.

5 0
3 years ago
A city has a population of 310,000 people. Suppose that each year the population grows by 9%. What will the population be after
Leno4ka [110]

Answer: 644,800

Step-by-step explanation:

This can also be solved using the terms of Arithmetic Progressions.

Let the 13 years be number of terms of the sequences (n)

Therefore ;

T₁₃              = a + ( n - 1 )d , where a = 310,000 and d = 9% of 310,000

9% of 310,000 = 9/100 x 310,000

                        = 27,900

so the common difference (d)

                     d = 27,900

Now substitute for the values  in the formula above and calculate

T₁₃              = 310,000 + ( 13 - 1 ) x 27,900

                  = 310,000 + 12 x 27,900

                  = 310,000 + 334,800

                  = 644,800.

The population after 13 years = 644,800.

 

3 0
3 years ago
What is the value of k in the equation 5k-2k=12
Mamont248 [21]

Answer:

k =4

Step-by-step explanation:

5k-2k=12

Combine like terms

3k = 12

Divide each side by 3

3k/3 = 12/3

k = 4

5 0
3 years ago
Read 2 more answers
What type of reaction is shown below? Check all that apply. 2Na + Cl2 → 2NaCl synthesis decomposition combustion
const2013 [10]

Answer: This is a type of Synthesis reaction.

Explanation:

  • Synthesis reaction is a type of chemical reaction in which two or more substances combine to form a single substance.

A+B\rightarrow AB

  • Decomposition reactions are a type of chemical reactions in which a substance breaks down into two or more substances.

AB\rightarrow A+B

  • Combustion reaction is a type of chemical reaction in which a hydrocarbon reacts with oxygen gas to produce carbon dioxide and water.

Hydrocarbon+O_2\rightarrow H_2O+CO_2

For the given reaction:

2Na(s)+Cl_2(g)\rightarrow 2NaCl

Here, 2 substances are combining together to form a single substance. Hence, it is considered as a synthesis reaction.

8 0
3 years ago
Read 2 more answers
)How many triangles can be made if one angle is 95° and another angle is acute?
OlgaM077 [116]
More than 2 ... there is a right and a obtuse i think 
7 0
3 years ago
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