Use the fact that to prove Chebyshev’s inequality given in Exercise 44.

Answer : Step 1 : 2 2 From the given information we have to prove (x ) P(x) (x ) P(x). all x x | | k It is given (x ) P(x) (x ) P(x) ...1) all x x|: | k Let SKset of variable lies betwexn ±xKS Where S x standard deviation xS = ) 2 Chebyshev’s inequality P( | |) 2 2 2 2 2 = (t ) p(t) dt (t ) p (x) dt + (t ) p (x) dt + From equation 1 is given by. Where = t p (t) dt + p (t) dt x x + 2 p (t) dt + p (t) dt x x + 2 2 P( x | ) | 2 2 Therefore (x ) P(x) (x ) P(x) all x x : |x| k