Question

Exercise 2 Consider a random variable X with E]5 and VarX 16 (a) Calculate P(lz-5 < 6) if X follows a normal distribution. (b) Use Chebyshev's inequality to provide a lower bound for P(-5). (No longer assume X is normal.)

Answer 1

a) here std deviation =(16)^1/2 =4

for normal distribution z score =(X-μ)/σ
here mean=       μ=	5
std deviation   =σ=	4.0000

hence P(|X-5|<6) =P(-6<X-5<6) =P(-1<X<11) =P(-1.5<Z<1.5)=

0.9332-0.0668=

0.8664

b)

from Chebyshev's: P(|X-5|<6) =P(-6<X-5<6) =P(-1<X<11) =P(-1.5<Z<1.5) =(1-1/1.5²) =1-0.4444 =0.5556