# How to find E(1/X)?

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

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

#for discrete pdf

so

putting this into a table for ease of calculation

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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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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.

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.

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.

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