Geometric distribution

Question 1

P( X = x) = ?

Answer 1

P( X = x) = [q^(x-1)] p

Question 2

X = ?

Answer 2

X : a variable

Question 3

x = ?

Answer 3

x : the specific drop for the success event

Question 4

q = ?

Answer 4

probability that event will fail

Question 5

p = ?

Answer 5

probability of a successful event

Question 6

mean = μέση τιμή = ?

Answer 6

μ = 1/p

Question 7

variance = διακύμανση = ?

Answer 7

Var(x) = σ^2 = (1/p) [ (1/p) - 1)] = μ (μ-1)

Question 8

standard deviation = τυπική απόκλιση = ?

Answer 8

σ = [ Var(x) ]^ 1/2 = (σ^2)^1/2

Question 9

F(x) = cumulative geometric distribution = αθροιστική γεωμετρική κατανομή = ?

Answer 9

F(x) = P( X <= x) = 1-q^x

Question 10

P(X < 5) = ?

Answer 10

P(X < 5( = P(X <= 4) (otherwise i cannot use the above formula.

Question 11

P(X > 12) = ?

Answer 11

P(X > 12) = 1 - P(X <= 12) (apo sxima geometrikis katanomis)

Question 12

P(X >= 12) = ?

Answer 12

P(X >= 12) = P(X > 11)

Question 13

P(15 <= X <= 30) = >

Answer 13

P(15 <= X <= 30) = 1 - P(X <= 14) - P(X >= 31) (apo sxima geometrikis katanomis)

Question 14

P(X > x) = ?

Answer 14

P(X > x) = 1 - P(X > x) = 1 - (1 - q^x) = q^x

Question 15

P(X >= x) = ?

Answer 15

P(X >= x) = q^(x-1) (iso me to P(X > x) = q^x, apla gia allo x)

Question 16

P(X < x) = ?

Answer 16

P(X < x) =1 - q^(x-1) (iso me to P(X <= x) = 1 - q^x, apla gia allo x)

Question 17

σ = ? (άλλος τύπος) = τυπική απόκλιση

Answer 17

σ = [ (1-p) / p^2 ] ^1/2