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Consider a random variable X such that P(X= -1) = P(X= 1) = ½

a. Compute E(x)

b. Compute var(x)

c. Compute P(/X-μ/≥1)

d. Show that Chebyshev's inequality is an equality for P(/X-μ/≥1).

 Apr 18, 2015

Best Answer 

 #1
avatar+28457 
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a.  E(x) = (1/2)*(-1) + (1/2)*(1) = 0

 

b. var(x) = ((-1 - 0)2 + (1 - 0)2)/2 = 1

 

c. P(|x - E(x)|>1) = 0,     P(|x - E(x)|=1) =   1

 

d.  See c.

 Apr 19, 2015
 #1
avatar+28457 
+5
Best Answer

a.  E(x) = (1/2)*(-1) + (1/2)*(1) = 0

 

b. var(x) = ((-1 - 0)2 + (1 - 0)2)/2 = 1

 

c. P(|x - E(x)|>1) = 0,     P(|x - E(x)|=1) =   1

 

d.  See c.

Alan Apr 19, 2015

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