there are 4 cards numbered 1 to 4 one number on one card . 2 cards are drawn at random without replacement . let x denote the sum of numbers on the 2 drawn cards . find the mean and varience of x

 

Asked by alanpeter9611 | 12th Feb, 2019, 05:18: PM

Expert Answer:

f o l l o w i n g space s u m s space a r e space p o s s i b l e space 3 comma 4 comma 5 comma 6 comma 7
table row straight x 3 4 5 6 7 row cell straight P left parenthesis straight x right parenthesis end cell cell 2 over 12 end cell cell 2 over 12 end cell cell 4 over 12 end cell cell 2 over 12 end cell cell 2 over 12 end cell end table

table row cell straight x. straight P left parenthesis straight x right parenthesis end cell cell 3 over 6 end cell cell 4 over 6 end cell cell 5 over 3 end cell cell 6 over 6 end cell cell 7 over 6 end cell row cell straight x squared. straight P left parenthesis straight x right parenthesis end cell cell 9 over 6 end cell cell 16 over 6 end cell cell 25 over 3 end cell cell 36 over 6 end cell cell 49 over 6 end cell end table

m e a n equals begin inline style sum for blank of end style straight x. straight P left parenthesis straight x right parenthesis equals 30 over 6 equals 5
v a r i a n c e equals begin inline style stack sum straight x squared. straight P left parenthesis straight x right parenthesis with blank below end style minus begin inline style open parentheses sum for blank of straight x. straight P left parenthesis straight x right parenthesis close parentheses end style squared equals 160 over 6 minus 25 equals 5 over 3

Answered by Arun | 13th Feb, 2019, 11:01: AM