Question

Let $\{X(t), t \ge 0\}$ be a pure birth process with rates $\lambda_k = k^2$, starting with $X(0) = 1$. Let $Y(t) = min(X(t), 3)$. Find out the mean of $\int_0^T Y(t)dt$, where $T$ is a random variable uniformly distributed on $[0, 1]$ and independent of the pure birth process.

Name: let xtt0 be a pure birth process with rates lambda kk2 starting with x01 let ytminxt3 find out the mean of int0t ytdt where t is a random variable uniformly distributed on 01 and independe 21289
Uploaded: 2021-12-11T04:13:35-08:00
Duration: 4 min 38 s
Channel: Narayan Hari
Description: let xtt0 be a pure birth process with rates lambda kk2 starting with x01 let ytminxt3 find out the mean of int0t ytdt where t is a random variable uniformly distributed on 01 and independe 21289

          Let $\{X(t), t \ge 0\}$ be a pure birth process with rates $\lambda_k = k^2$, starting with $X(0) = 1$. Let $Y(t) = min(X(t), 3)$. Find out the mean of $\int_0^T Y(t)dt$, where $T$ is a random variable uniformly distributed on $[0, 1]$ and independent of the pure birth process.

let xtt0 be a pure birth process with rates lambda kk2 starting with x01 let ytminxt3 find out the mean of int0t ytdt where t is a random variable uniformly distributed on 01 and independe 21289

Added by Erika S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Narayan Hari

12/11/2021

Step 1

Since $T$ is uniformly distributed on $[0, 1]$, we can use the following formula: $$E[\int_0^T Y(t)dt] = \int_0^1 E[Y(t)]dt$$ Show more…

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Let $\{X(t), t \ge 0\}$ be a pure birth process with rates $\lambda_k = k^2$, starting with $X(0) = 1$. Let $Y(t) = min(X(t), 3)$. Find out the mean of $\int_0^T Y(t)dt$, where $T$ is a random variable uniformly distributed on $[0, 1]$ and independent of the pure birth process.