Laplace transform of exponential distributed random varibale
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0
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Let $Tsim Exp(lambda)$. I want to calculate the laplace transform
$$E[e^{-delta T}]$$
So far I get $$E[e^{-delta T}]=int_0^infty e^{-delta x}lambda e^{-lambda x}dx=lambdaint_0^infty e^{-(delta+lambda) x}dx=lambdacdotbigg[-frac{1}{delta+lambda}e^{-(delta+lambda)x}bigg]_0^infty=frac{lambda}{delta+lambda}$$
Is this right?
probability functional-analysis probability-theory
asked 10 hours ago
user408858
15810
add a comment |
up vote
0
down vote
favorite
Let $Tsim Exp(lambda)$. I want to calculate the laplace transform
$$E[e^{-delta T}]$$
So far I get $$E[e^{-delta T}]=int_0^infty e^{-delta x}lambda e^{-lambda x}dx=lambdaint_0^infty e^{-(delta+lambda) x}dx=lambdacdotbigg[-frac{1}{delta+lambda}e^{-(delta+lambda)x}bigg]_0^infty=frac{lambda}{delta+lambda}$$
Is this right?
probability functional-analysis probability-theory
asked 10 hours ago
user408858
15810
1
Search for "moment generating function of exponential distribution".
– StubbornAtom
10 hours ago
Why you don't just write yes!?
– Stockfish
10 hours ago
His comment was before my edit. ;-) So I consider it being right now, thank you.
– user408858
10 hours ago
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let $Tsim Exp(lambda)$. I want to calculate the laplace transform
$$E[e^{-delta T}]$$
So far I get $$E[e^{-delta T}]=int_0^infty e^{-delta x}lambda e^{-lambda x}dx=lambdaint_0^infty e^{-(delta+lambda) x}dx=lambdacdotbigg[-frac{1}{delta+lambda}e^{-(delta+lambda)x}bigg]_0^infty=frac{lambda}{delta+lambda}$$
Is this right?
probability functional-analysis probability-theory
asked 10 hours ago
user408858
15810
Let $Tsim Exp(lambda)$. I want to calculate the laplace transform
$$E[e^{-delta T}]$$
So far I get $$E[e^{-delta T}]=int_0^infty e^{-delta x}lambda e^{-lambda x}dx=lambdaint_0^infty e^{-(delta+lambda) x}dx=lambdacdotbigg[-frac{1}{delta+lambda}e^{-(delta+lambda)x}bigg]_0^infty=frac{lambda}{delta+lambda}$$
Is this right?
probability functional-analysis probability-theory
probability functional-analysis probability-theory
asked 10 hours ago
user408858
15810
asked 10 hours ago
user408858
15810
edited 10 hours ago
asked 10 hours ago
user408858
15810
asked 10 hours ago
user408858
15810
asked 10 hours ago
user408858
15810
15810
1
Search for "moment generating function of exponential distribution".
– StubbornAtom
10 hours ago
Why you don't just write yes!?
– Stockfish
10 hours ago
His comment was before my edit. ;-) So I consider it being right now, thank you.
– user408858
10 hours ago
add a comment |
1
Search for "moment generating function of exponential distribution".
– StubbornAtom
10 hours ago
Why you don't just write yes!?
– Stockfish
10 hours ago
His comment was before my edit. ;-) So I consider it being right now, thank you.
– user408858
10 hours ago
1
1
Search for "moment generating function of exponential distribution".
– StubbornAtom
10 hours ago
Search for "moment generating function of exponential distribution".
– StubbornAtom
10 hours ago
Why you don't just write yes!?
– Stockfish
10 hours ago
Why you don't just write yes!?
– Stockfish
10 hours ago
His comment was before my edit. ;-) So I consider it being right now, thank you.
– user408858
10 hours ago
His comment was before my edit. ;-) So I consider it being right now, thank you.
– user408858
10 hours ago
add a comment |
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1
Search for "moment generating function of exponential distribution".
– StubbornAtom
10 hours ago
Why you don't just write yes!?
– Stockfish
10 hours ago
His comment was before my edit. ;-) So I consider it being right now, thank you.
– user408858
10 hours ago