To calculate the Poisson distribution and the theoretical frequency, we first need to calculate the mean (λ) of the distribution. The mean can be calculated by multiplying each number of accidents by the number of days it occurs, summing these products, and then dividing by the total number of days.

Here's how to calculate the mean:

λ = (0*21 + 1*18 + 2*7 + 3*3 + 4*1) / 50 = 0.86

Now, we can calculate the Poisson probabilities for 0, 1, 2, 3, and 4 accidents. The formula for the Poisson probability is:

P(x; λ) = e^-λ * λ^x / x!

where:
- e is the base of the natural logarithm (approximately 2.71828),
- λ is the mean number of successes that result from the experiment,
- x is the actual number of successes that result from the experiment, and
- x! is the factorial of x.

Using this formula, we get:

P(0; 0.86) = e^-0.86 * 0.86^0 / 0! = 0.423
P(1; 0.86) = e^-0.86 * 0.86^1 / 1! = 0.364
P(2; 0.86) = e^-0.86 * 0.86^2 / 2! = 0.157
P(3; 0.86) = e^-0.86 * 0.86^3 / 3! = 0.045
P(4; 0.86) = e^-0.86 * 0.86^4 / 4! = 0.010

These are the Poisson probabilities. To find the theoretical frequencies, we multiply these probabilities by the total number of days (50):

Theoretical frequency for 0 accidents = 0.423 * 50 = 21.15
Theoretical frequency for 1 accident = 0.364 * 50 = 18.2
Theoretical frequency for 2 accidents = 0.157 * 50 = 7.85
Theoretical frequency for 3 accidents = 0.045 * 50 = 2.25
Theoretical frequency for 4 accidents = 0.010 * 50 = 0.5

So, the theoretical frequencies are approximately 21.15, 18.2, 7.85, 2.25, and 0.5 for 0, 1, 2, 3, and 4 accidents, respectively.

Question

To calculate the Poisson distribution and the theoretical frequency, we first need to calculate the mean (λ) of the distribution. The mean can be calculated by multiplying each number of accidents by the number of days it occurs, summing these products, and then dividing by the total number of days.

Here's how to calculate the mean:

λ = (0*21 + 1*18 + 2*7 + 3*3 + 4*1) / 50 = 0.86

Now, we can calculate the Poisson probabilities for 0, 1, 2, 3, and 4 accidents. The formula for the Poisson probability is:

P(x; λ) = e^-λ * λ^x / x!

where:
- e is the base of the natural logarithm (approximately 2.71828),
- λ is the mean number of successes that result from the experiment,
- x is the actual number of successes that result from the experiment, and
- x! is the factorial of x.

Using this formula, we get:

P(0; 0.86) = e^-0.86 * 0.86^0 / 0! = 0.423
P(1; 0.86) = e^-0.86 * 0.86^1 / 1! = 0.364
P(2; 0.86) = e^-0.86 * 0.86^2 / 2! = 0.157
P(3; 0.86) = e^-0.86 * 0.86^3 / 3! = 0.045
P(4; 0.86) = e^-0.86 * 0.86^4 / 4! = 0.010

These are the Poisson probabilities. To find the theoretical frequencies, we multiply these probabilities by the total number of days (50):

Theoretical frequency for 0 accidents = 0.423 * 50 = 21.15
Theoretical frequency for 1 accident = 0.364 * 50 = 18.2
Theoretical frequency for 2 accidents = 0.157 * 50 = 7.85
Theoretical frequency for 3 accidents = 0.045 * 50 = 2.25
Theoretical frequency for 4 accidents = 0.010 * 50 = 0.5

So, the theoretical frequencies are approximately 21.15, 18.2, 7.85, 2.25, and 0.5 for 0, 1, 2, 3, and 4 accidents, respectively.

Knowee AI · Accepted Answer

To calculate the Poisson distribution and the theoretical frequency, we first need to calculate the mean (λ) of the distribution. The mean can be calculated by multiplying each number of accidents by the number of days it occurs, summing these products, and then dividing by the total number of days.

Here's how to calculate the mean:

λ = (0*21 + 1*18 + 2*7 + 3*3 + 4*1) / 50 = 0.86

Now, we can calculate the Poisson probabilities for 0, 1, 2, 3, and 4 accidents. The formula for the Poisson probability is:

P(x; λ) = e^-λ * λ^x / x!

where:
- e is the base of the natural logarithm (approximately 2.71828),
- λ is the mean number of successes that result from the experiment,
- x is the actual number of successes that result from the experiment, and
- x! is the factorial of x.

Using this formula, we get:

P(0; 0.86) = e^-0.86 * 0.86^0 / 0! = 0.423
P(1; 0.86) = e^-0.86 * 0.86^1 / 1! = 0.364
P(2; 0.86) = e^-0.86 * 0.86^2 / 2! = 0.157
P(3; 0.86) = e^-0.86 * 0.86^3 / 3! = 0.045
P(4; 0.86) = e^-0.86 * 0.86^4 / 4! = 0.010

These are the Poisson probabilities. To find the theoretical frequencies, we multiply these probabilities by the total number of days (50):

Theoretical frequency for 0 accidents = 0.423 * 50 = 21.15
Theoretical frequency for 1 accident = 0.364 * 50 = 18.2
Theoretical frequency for 2 accidents = 0.157 * 50 = 7.85
Theoretical frequency for 3 accidents = 0.045 * 50 = 2.25
Theoretical frequency for 4 accidents = 0.010 * 50 = 0.5

So, the theoretical frequencies are approximately 21.15, 18.2, 7.85, 2.25, and 0.5 for 0, 1, 2, 3, and 4 accidents, respectively.

The following tables gives the number of days in a 50 days period during which an automobile accident occurs in a cityNo. of accident: 0 1 2 3 4No. of days: 21 18 7 3 1Find the Poisson distribution and calculate the Theoretical frequency

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