germany-abitur 2023 QB 1d

germany-abitur · Other · abitur__bayern_stochastik 3 marks Measures of Location and Spread
For a certain value $n \in \{ 1 ; 2 ; 3 ; \ldots \}$, the binomially distributed random variables $Z _ { p }$ with parameters $n$ and $p$ are considered for $p \in ] 0 ; 1 [$. Show that among these random variables, the one with $p = 0.5$ has the greatest variance. 
For a certain value $n \in \{ 1 ; 2 ; 3 ; \ldots \}$, the binomially distributed random variables $Z _ { p }$ with parameters $n$ and $p$ are considered for $p \in ] 0 ; 1 [$. Show that among these random variables, the one with $p = 0.5$ has the greatest variance.
Paper Questions
QA a QA b QB 1a QB 1b QB 1c QB 1d QB 1e QB 2 QB 3a QB 3b