exercise:3a96777f2a: Difference between revisions
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Let <math>X</math> be a random variable with <math>E(X) = \mu</math> and <math>Var(X) = \sigma^2</math>. Suppose <math display = "block">E[(X-c_0)^2] \leq E[(X-c)^2]</math> for all <math>c</math>. Determine <math>E[(X-c_0)^2] </math>. | Let <math>X</math> be a random variable with <math>E(X) = \mu</math> and <math>Var(X) = \sigma^2</math>. Suppose <math display = "block">E[(X-c_0)^2] \leq E[(X-c)^2]</math> for all <math>c</math>. Determine <math>E[(X-c_0)^2] </math>. | ||
<ul class="mw-excansopts"> | |||
<li><math>\frac{\sigma^2}{2}</math></li> | |||
<li><math>\mu^2</math></li> | |||
<li><math>\sigma^2</math></li> | |||
<li><math>\min(\sigma^2,\mu^2)</math></li> | |||
<li><math>\frac{\sigma^2 + \mu^2}{2}</math></li> | |||
</ul> | |||
Latest revision as of 01:05, 25 June 2024
Let [math]X[/math] be a random variable with [math]E(X) = \mu[/math] and [math]Var(X) = \sigma^2[/math]. Suppose
[[math]]E[(X-c_0)^2] \leq E[(X-c)^2][[/math]]
for all [math]c[/math]. Determine [math]E[(X-c_0)^2] [/math].
- [math]\frac{\sigma^2}{2}[/math]
- [math]\mu^2[/math]
- [math]\sigma^2[/math]
- [math]\min(\sigma^2,\mu^2)[/math]
- [math]\frac{\sigma^2 + \mu^2}{2}[/math]