I need urgent help with this please. Consider the following sentence: \"The quic

Question

I need urgent help with this please.

Consider the following sentence: "The quick brown fox jumped over the lazy dog," Two distinct words are randomly selected from this sentence and X represents the total length of the two words. For example, if the words were "The" and "quick", then X 8 For the purpose of this problem, we will treat "The" and "the as distinct words (a) What values can X take on? (b) Write down the probability mass function of X (c) What is the expected total length of the two words?

Explanation / Answer

here from above

from above it can be seen that X can take Values =6,7,8,9,10.11.12

b)from above table in P(X) column PMF of X been given

C) expected value of X=8

word1 Word2 Length1 Length2 X=L1+L2 The The 3 3 6 quick The 5 3 8 brown The 5 3 8 fox The 3 3 6 jumped The 6 3 9 over The 4 3 7 the The 3 3 6 lazy The 4 3 7 dog The 3 3 6 The quick 3 5 8 quick quick 5 5 10 brown quick 5 5 10 fox quick 3 5 8 jumped quick 6 5 11 over quick 4 5 9 the quick 3 5 8 lazy quick 4 5 9 dog quick 3 5 8 The brown 3 5 8 quick brown 5 5 10 brown brown 5 5 10 fox brown 3 5 8 jumped brown 6 5 11 over brown 4 5 9 the brown 3 5 8 lazy brown 4 5 9 dog brown 3 5 8 The fox 3 3 6 quick fox 5 3 8 brown fox 5 3 8 fox fox 3 3 6 jumped fox 6 3 9 over fox 4 3 7 the fox 3 3 6 lazy fox 4 3 7 dog fox 3 3 6 The jumped 3 6 9 quick jumped 5 6 11 brown jumped 5 6 11 fox jumped 3 6 9 jumped jumped 6 6 12 over jumped 4 6 10 the jumped 3 6 9 lazy jumped 4 6 10 dog jumped 3 6 9 The over 3 4 7 quick over 5 4 9 brown over 5 4 9 fox over 3 4 7 jumped over 6 4 10 over over 4 4 8 the over 3 4 7 lazy over 4 4 8 dog over 3 4 7 The the 3 3 6 quick the 5 3 8 brown the 5 3 8 fox the 3 3 6 jumped the 6 3 9 over the 4 3 7 the the 3 3 6 lazy the 4 3 7 dog the 3 3 6 The lazy 3 4 7 quick lazy 5 4 9 brown lazy 5 4 9 fox lazy 3 4 7 jumped lazy 6 4 10 over lazy 4 4 8 the lazy 3 4 7 lazy lazy 4 4 8 dog lazy 3 4 7 The dog 3 3 6 quick dog 5 3 8 brown dog 5 3 8 fox dog 3 3 6 jumped dog 6 3 9 over dog 4 3 7 the dog 3 3 6 lazy dog 4 3 7 dog dog 3 3 6

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