Once again consider a spacecraft which performs scientific observations in a loc

Question

Once again consider a spacecraft which performs scientific observations in a location far far away. During a day it will finish 100 observations. Since the communication window is very lim- ited, an on-board computer will do a pre-processing step and decide which observations should be transmitted back to Earth and the rest will be eliminated. You are interested in the total amount of data to be transmitted, and conclude that this amount in each observation follows an unknown distribution with average 100KB and standard deviation 5KB, and the pre-processing will evaluate each observation independently and mark it for transmission with probability 10%. i. What is the average amount of data that will need to be ii. What is its variance? in a day?

Explanation / Answer

Question 1

Here the average amount of data that will need to be transmitted in a day = average amount of data in one transmission * number of transmission = 100 KB * 100 = 10000 KB

there is 10% probability that it will be marked for transmission so total transmitted data = 10000 * 0.10 = 1000 KB

(b) Here variance of amount of data in one transmission = sqrt (0.10 * 0.90 * 100) = 3KB

so variance of amount of data in 100 transmission = sqrt (3 * 3 * 100) = 30 KB

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