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zepelin [54]
3 years ago
12

Assume that the Poisson distribution applies and that the mean number of aircraft accidents is 9 per month. Find​ P(0), the prob

ability that in a​ month, there will be no aircraft accidents. Is it unlikely to have a month with no aircraft​ accidents?
Mathematics
1 answer:
Ugo [173]3 years ago
5 0

Answer: 0.0001

It is unlikely to have a month with no aircraft​ accidents .

Step-by-step explanation:

Given :  Mean number of aircraft accidents = 9 per month

The Poisson distribution formula :-

\dfrac{e^{-\lambda}\lambda^x}{x!}, where \lambda is the mean of the distribution.

If X = the number of aircraft accidents per month, then the probability that in a​ month, there will be no aircraft accidents will be :-

\dfrac{e^{-9}(9)^0}{0!}=0.000123409804087\approx0.0001

Hence, the probability that in a​ month, there will be no aircraft accidents = 0.0001

Since this is less than 0.5 , therefor it is unlikely to have a month with no aircraft​ accidents .

You might be interested in
Sin4u=2sin 2u cos 2u​
yKpoI14uk [10]

Answer:

If you've learnt sin(A+B) = sinAcosB + cosAsinB,

sin(4u)

= sin(2u+2u)

= sin(2u)cos(2u) + cos(2u)sin(2u)

= 2 sin(2u) cos(2u).

4 0
3 years ago
(a) Let R = {(a,b): a² + 3b <= 12, a, b € z+} be a relation defined on z+)
grin007 [14]

Answer:

R is an equivalence relation, since R is reflexive, symmetric, and transitive.

Step-by-step explanation:

The relation R is an equivalence if it is reflexive, symmetric and transitive.

The order to options required to show that R is an equivalence relation are;

((a, b), (a, b)) ∈ R since a·b = b·a

Therefore, R is reflexive

If ((a, b), (c, d)) ∈ R then a·d = b·c, which gives c·b = d·a, then ((c, d), (a, b)) ∈ R

Therefore, R is symmetric

If ((c, d), (e, f)) ∈ R, and ((a, b), (c, d)) ∈ R therefore, c·f = d·e, and a·d = b·c

Multiplying gives, a·f·c·d = b·e·c·d, which gives, a·f = b·e, then ((a, b), (e, f)) ∈R

Therefore R is transitive

From the above proofs, the relation R is reflexive, symmetric, and transitive, therefore, R is an equivalent relation.

Reasons:

Prove that the relation R is reflexive

Reflexive property is a property is the property that a number has a value that it posses (it is equal to itself)

The given relation is ((a, b), (c, d)) ∈ R if and only if a·d = b·c

By multiplication property of equality; a·b = b·a

Therefore;

((a, b), (a, b)) ∈ R

The relation, R, is reflexive.

Prove that the relation, R, is symmetric

Given that if ((a, b), (c, d)) ∈ R then we have, a·d = b·c

Therefore, c·b = d·a implies ((c, d), (a, b)) ∈ R

((a, b), (c, d)) and ((c, d), (a, b)) are symmetric.

Therefore, the relation, R, is symmetric.

Prove that R is transitive

Symbolically, transitive property is as follows; If x = y, and y = z, then x = z

From the given relation, ((a, b), (c, d)) ∈ R, then a·d = b·c

Therefore, ((c, d), (e, f)) ∈ R, then c·f = d·e

By multiplication, a·d × c·f = b·c × d·e

a·d·c·f = b·c·d·e

Therefore;

a·f·c·d = b·e·c·d

a·f = b·e

Which gives;

((a, b), (e, f)) ∈ R, therefore, the relation, R, is transitive.

Therefore;

R is an equivalence relation, since R is reflexive, symmetric, and transitive.

Based on a similar question posted online, it is required to rank the given options in the order to show that R is an equivalence relation.

Learn more about equivalent relations here:

brainly.com/question/1503196

4 0
2 years ago
Tom is 10 years younger than Becky. In two years, Becky will be twice as old as Tom. How old is Tom now?
qwelly [4]

Answer:

20

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Simplify by dividing (-3/8) -5/9
Elodia [21]

Answer:

\frac{-27}{40}

Step-by-step explanation:

(\frac{-3}{8})÷\frac{5}{9}

\frac{-3}{8}×\frac{9}{5}

\frac{-27}{40}

6 0
3 years ago
Do this for me and I will give 42 points, it is 9th grade prob and stats.
Hitman42 [59]

answer what question?

6 0
3 years ago
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