answer number 1 only 3.5.8Laplace DistributionDefinition 50We will say that a random variable X has Laplace distribution if its density is given by-이|피Show that this equationis a valid density.f(1)(3.15)e2with 0 > 0. We will denote X ~ Laplace(0).x is any real numberteta is any positive numberShow all necessary solutions.1. Let f(r) = c(1– |2|)1|–1,1)(2x).(a) Find the constant e that makes f a probability density function.(b) Compute E(X) and Var(X).2. Prove Proposition 40.3. Prove Proposition 41.

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Description: answer number 1 only 3.5.8Laplace DistributionDefinition 50We will say that a random variable X has Laplace distribution if its density is given by-이|피Show that this equationis a valid density.f(1)(3.15)e2with 0 > 0. We will denote X ~ Laplace(0).x i

Calculate the probability that the random variable X is Real. PX∈R=∫-∞∞fxdx…

Answered: 1. Let f(x) = c(1- |r|)1|-1,1|(x). (a)…

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1. Let f(x) = c(1- |r|)1|-1,1|(x). (a) Find the constant c that makes f a probability density function. (b) Compute E(X) and Var(X).

Linear Algebra: A Modern Introduction

4th Edition

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Author:David Poole

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Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

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answer number 1 only

3.5.8
Laplace Distribution
Definition 50
We will say that a random variable X has Laplace distribution if its density is given by
-이|피
Show that this equation
is a valid density.
f(1)
(3.15)
e
2
with 0 > 0. We will denote X ~ Laplace(0).
x is any real number
teta is any positive number
Show all necessary solutions.
1. Let f(r) = c(1– |2|)1|–1,1)(2x).
(a) Find the constant e that makes f a probability density function.
(b) Compute E(X) and Var(X).
2. Prove Proposition 40.
3. Prove Proposition 41.

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