Thread: expected value with variables!

first part:

A box contains 7 black cubes and 3 red cubes. Debra selects three cubes from the box without replacement. Let random variable N denote the number of red cubes selected by Debra.

second part:

Debra will win $2.00 for every red cube selected and lose $1.00 for every black cube selected. Let the random variable W denote Debra's winnings.
If W=aN+b, find a and b. Hence, find E(W)



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I'm okay with the first part ...but I'm not sure how to approach the second part.


Help please!

Originally Posted by shawli

first part:

A box contains 7 black cubes and 3 red cubes. Debra selects three cubes from the box without replacement. Let random variable N denote the number of red cubes selected by Debra.

second part:

Debra will win $2.00 for every red cube selected and lose $1.00 for every black cube selected. Let the random variable W denote Debra's winnings.
If W=aN+b, find a and b. Hence, find E(W)



---------------------------------

I'm okay with the first part ...but I'm not sure how to approach the second part.


Help please!

W = (2)(N) - (1)(3 - N) = ....

E(aN + b) = a E(N) + b.