probability II, Statistics

The pdf of exponential distribution is f(x)= -----

• e^-λx , x≥0

• λe^-λx , x≥0

• e^λx , x≥0

• e^-λ , x≥0

The mean , variance of exponential distribution is ------

• 1/λ, 1/λ²

• λ, 1/λ²

• λ, λ²

• 1/λ, λ²

The memoryless property of exponential distribution is----

• P(X>s+t/X>s)= P(X>t)

• P(X>s-t/X>s)= P(X>t)

• P(X>t/X>s)= P(X>t)

• P(X>st/X>s)= P(X>t)

The pdf of gamma distribution is ,f(x) =-----

• λ^k x^k-1 e^-λx _/ Γk , x≥0

• λ^k x^ke^-λx , x≥0

• λ^k-1 x^k-1 e^-λx _/ Γk , x≥0

• λ^k x^k-1 e^λx ,x≥0

The mean , varaince of gamma distribution is ----

• k/λ ,k/λ²

• k/λ ,k

• 1/λ ,k/λ²

• k/λ ,1/λ²

The first moment about the mean is ------

• 1

• 0

• 2

• 3

The second moment about the mean is ----

• mean

• variance

• kurtosis

• skewness

If β₂ = 3 then the curve is ----

• platykurtic

• mesokurtic

• leptokurtic

• kurtic

If β₂ < 3 then the curve is ----

• mesokurtic

• platykurtic

• leptokurtic

• kurtic

If β₂ > 3 then the curve is ----

• mesokurtic

• leptokurtic

• platykurtic

• kurtic