h**********y
发帖数: 41 | 1 Suppose we toss a fear coin, and let N denote the number of tosses until we
get a head (including the final toss). What is E(N) and Var(N)?
I know E(N)=0.5*1+0.5*( E(N)+1 ), so E(N)=2.
Can I use this way to calculate Var(N)?
I know there is a solution in Joshi's red book, but that looks complicated,
Any other method to calculate Var(N)? | D********n
发帖数: 978 | 2 首先，请LZ原谅，本人实在无法忍受您用N来代表random variable的做法(这类似于给
一个女孩起名叫李刚)。本人用X代替。
注意到:
E(X^2) = 1/2*1^2 + 1/2*E((1+X)^2)，推理和你用来算E(X)一模一样。
可以解得E(X^2) = 6.
因此Var(X) = E(X^2) - E(X)^2 = 2.
we
,
【在 h**********y 的大作中提到】
: Suppose we toss a fear coin, and let N denote the number of tosses until we
: get a head (including the final toss). What is E(N) and Var(N)?
: I know E(N)=0.5*1+0.5*( E(N)+1 ), so E(N)=2.
: Can I use this way to calculate Var(N)?
: I know there is a solution in Joshi's red book, but that looks complicated,
: Any other method to calculate Var(N)?
| T*******t
发帖数: 9274 | 3 hoho
【在 D********n 的大作中提到】
: 首先，请LZ原谅，本人实在无法忍受您用N来代表random variable的做法(这类似于给
: 一个女孩起名叫李刚)。本人用X代替。
: 注意到:
: E(X^2) = 1/2*1^2 + 1/2*E((1+X)^2)，推理和你用来算E(X)一模一样。
: 可以解得E(X^2) = 6.
: 因此Var(X) = E(X^2) - E(X)^2 = 2.
:
: we
: ,
|
|
