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How to find E(1/X)?

Can someone please explain to me how to do question 7d? Thanks heaps!

Answer 1

Jonathan Allen

#0.12(2dp)#

#for discrete pdf

#E(f(x))=sum_(all" " x)f(x)P(X=x)#

#E(1/x)=sum_(all" "x)(1/x)P(X=x)#

putting this into a table for ease of calculation

#E(1/X)=0.005+0.838383..+0.01+0.006+0.0066#

#E(1/X)=0.1150..=0.12 (2dp)#

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Answer 2

Emery Adams

To find ( E(1/X) ), where ( X ) is a random variable:

Determine the probability distribution of ( X ), denoted by ( f_X(x) ).
Substitute ( 1/X ) into the expression for ( E(X) ), which is given by ( E(X) = \int_{-\infty}^{\infty} x \cdot f_X(x) , dx ).
Integrate ( 1/X ) with respect to ( x ) over the range of possible values of ( X ) according to the distribution ( f_X(x) ).
Evaluate the integral to find ( E(1/X) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.