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Asked by Topperlearning User 20th August 2016, 11:46 AM
Answered by Expert
Answer:

G i v e n space m e a n equals 2.94
1 cross times 1 half plus 2 cross times 1 fifth plus 4 cross times 3 over 5 plus 2 k cross times 1 over 10 plus 3 k cross times 1 over 25 plus 5 k cross times 1 over 25 equals 2.94
k open parentheses 2 over 10 plus 3 over 25 plus 1 fifth close parentheses equals 2.94 minus open parentheses 1 half plus 2 over 5 plus 12 over 25 close parentheses
k open parentheses 26 over 50 close parentheses equals fraction numerator 294 minus 50 minus 40 minus 48 over denominator 100 end fraction
k equals fraction numerator 50 cross times 156 over denominator 26 cross times 100 end fraction equals 3
w i t h space k equals 3 space t h e space p r o b a b i l i t y space d i s t r i b u t i o n space b e c o m e s
space
space space space space space space X colon colon space space 1 space space space space space space space space space space 2 space space space space space space space space space space 4 space space space space space space space space space space space 6 space space space space space space space space space space space space 9 space space space space space space space space space space space space 15
P left parenthesis X right parenthesis colon colon space space space 1 half space space space space space 1 fifth space space space space space space 3 over 25 space space space space space 1 over 10 space space space space space space space 1 over 25 space space space space space space space space space 1 over 25
m e a n space E left parenthesis X right parenthesis equals 2.94
E left parenthesis X squared right parenthesis equals 1 cross times 1 half plus 4 cross times 1 fifth plus 16 cross times 3 over 25 plus 36 cross times 1 over 10 plus 81 cross times 1 over 25 plus 225 cross times 1 over 25
equals fraction numerator 25 plus 40 plus 96 plus 180 plus 162 plus 450 over denominator 50 end fraction equals 953 over 50 equals 19.06
V a r left parenthesis X right parenthesis equals E left parenthesis X squared right parenthesis minus left square bracket E left parenthesis X right parenthesis right square bracket squared
space space space space space space space space space space space space space space equals 19.06 minus 2.94 squared
space space space space space space space space space space space space space space space space equals 10.4164

Answered by Expert 20th August 2016, 1:46 PM
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