Moderate -0.8 This is a direct application of the variance formula Var(Y) = E(Y²) - [E(Y)]² = 1040 - 16² = 784, then SD = √784 = 28. It's a one-step recall question with all values given, requiring only substitution into a standard formula. The multiple-choice format further reduces difficulty.
2 The continuous random variable \(Y\) has probability density function \(\mathrm { f } ( y )\) where
$$\int _ { - \infty } ^ { \infty } y \mathrm { f } ( y ) \mathrm { d } y = 16 \text { and } \int _ { - \infty } ^ { \infty } y ^ { 2 } \mathrm { f } ( y ) \mathrm { d } y = 1040$$
Find the standard deviation of \(Y\)
Circle your answer. [0pt]
[1 mark]
28
32
784
1024
2 The continuous random variable $Y$ has probability density function $\mathrm { f } ( y )$ where
$$\int _ { - \infty } ^ { \infty } y \mathrm { f } ( y ) \mathrm { d } y = 16 \text { and } \int _ { - \infty } ^ { \infty } y ^ { 2 } \mathrm { f } ( y ) \mathrm { d } y = 1040$$
Find the standard deviation of $Y$
Circle your answer.\\[0pt]
[1 mark]\\
28\\
32\\
784\\
1024
\hfill \mbox{\textit{AQA Further AS Paper 2 Statistics 2022 Q2 [1]}}