Question

The first four moments of a distribution about 2 x are 1, 2.5, 5.5 and 16. Calculate the four moments about the mean.

Answer 1

Answer:

In math 6+8 is the answer

Answer 2

Answer:

Let rth moment of a variable x about 5 is μ′r=E(xi−5)rμr′=E(xi−5)r and let rth moment of x about its mean be μr=E(xi−x¯)r.μr=E(xi−x¯)r.

So, μ′1=2⇒E(xi)−5=2⇒E(xi)=x¯=2+5=7μ1′=2⇒E(xi)−5=2⇒E(xi)=x¯=2+5=7

So, first moment about mean =μ1=E(xi−x¯)=E(xi)−x¯=7−7=0...(1)μ1=E(xi−x¯)=E(xi)−x¯=7−7=0...(1)

2nd moment about mean =μ2=E(xi−x¯)2=E(xi−7)2=E[(xi−5)+(5−7)]2=E[(xi−5)−2]2=E(xi−5)2−4E(xi−5)+4=μ′2−4μ′1+4