What is λe^{-λx}*λ^2ye^{-λy} ?

The solution to λe^{-λx}*λ^2ye^{-λy} is λ^3e^{-λx-λy}y

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simplify λe^{-λx}*λ^2ye^{-λy}

simplify

λ e^{- λ x} \cdot λ^{2} y e^{- λ y}

λ^{3} e^{- λ x - λ y} y

Solution steps

λ e^{- λ x} λ^{2} y e^{- λ y}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

λ λ^{2} = λ^{1 + 2}

= e^{- λ x} λ^{1 + 2} y e^{- λ y}

Add the numbers:

1 + 2 = 3

= e^{- λ x} λ^{3} y e^{- λ y}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{- λ x} e^{- λ y} = e^{- λ x - λ y}

= λ^{3} y e^{- λ x - λ y}

2 (2 x^{4} (3 x^{3}))

\frac{2}{π}

y^{4} \cdot e^{3 y} \cdot e^{- 3 y}

(1000) (89.1 \cdot 1 0^{- 6})

e^{- 25 (0)}

What is λe^{-λx}*λ^2ye^{-λy} ?
The solution to λe^{-λx}*λ^2ye^{-λy} is λ^3e^{-λx-λy}y