Expression 9: "y" equals 5.5 left brace, 0.2 less than or equal to "x" less than or equal to 0.2 plus StartFraction, 0.7 Over "M" , EndFraction "n" , right brace Has graph. To audio trace, press ALT+T.y=5.50.2≤x≤0.2+0.7Mn
9
Expression 10: "y" equals 5.5 left brace, 0.2 plus StartFraction, 0.7 Over "M" , EndFraction "n" less than or equal to "x" less than or equal to 0.9 , right brace Has graph. To audio trace, press ALT+T.y=5.50.2+0.7Mn≤x≤0.9
10
Hidden Label: left parenthesis, 0.2 plus StartFraction, 0.7 Over "M" , EndFraction times left bracket, 0... "n" , right bracket , 5.5 , right parenthesis equals a list of points. 11 items Has graph. To audio trace, press ALT+T.0.2+0.7M·0...n,5.5
Label
equals=
left parenthesis, 0.2 , 5.5 , right parenthesis0.2,5.5
left parenthesis, 0.2 5 8 3 , 5.5 , right parenthesis0.2583,5.5
left parenthesis, 0.3 1 6 7 , 5.5 , right parenthesis0.3167,5.5
left parenthesis, 0.3 7 5 , 5.5 , right parenthesis0.375,5.5
left parenthesis, 0.4 3 3 3 , 5.5 , right parenthesis0.4333,5.5
left parenthesis, 0.4 9 1 7 , 5.5 , right parenthesis0.4917,5.5
left parenthesis, 0.5 5 , 5.5 , right parenthesis0.55,5.5
left parenthesis, 0.6 0 8 3 , 5.5 , right parenthesis0.6083,5.5
left parenthesis, 0.6 6 6 7 , 5.5 , right parenthesis0.6667,5.5
left parenthesis, 0.7 2 5 , 5.5 , right parenthesis0.725,5.5
left parenthesis, 0.7 8 3 3 , 5.5 , right parenthesis0.7833,5.5
11
`r=${r}` left parenthesis, 0.2 plus StartFraction, 0.7 Over "M" , EndFraction "r" , 5.5 , right parenthesis equals left parenthesis, 0.6 6 6 6 6 6 6 6 6 6 6 7 , 5.5 , right parenthesis Has graph. To audio trace, press ALT+T.0.2+0.7Mr,5.5
Label:
equals=
left parenthesis, 0.6 6 6 6 6 6 6 7 , 5.5 , right parenthesis0.66666667,5.5
Best guess for next-round probability of success is 0.75, not 0.8!
"p" equals StartFraction, "r" Over "n" , EndFraction equals 0.8p=rn=0.8
"f" ( "p" ) equals ( "n" plus 1 ) "p" Superscript, "r" , Baseline ( 1 minus "p" ) Superscript, "n" minus "r" , Baseline StartBinomial, "n" Choose "r" , EndBinomialf(p)=(n+1)pr(1−p)n−rnr
Start integral from 0 to 1, end integral, "f" ( "p" ) "d" "x" equals 1∫10f(p)dx=1
Start integral from 0 to 1, end integral, "p" "f" ( "p" ) "d" "x" equals StartFraction, "r" plus 1 Over "n" plus 2 , EndFraction equals 0.7 5∫10pf(p)dx=r+1n+2=0.75
So far, 8 out of 10 trials (0.8) have been successes.
Thus our best guess for
"p"p
is 0.8.
However, our best guess for the probability of the
