Mathematics, 12.12.2019 20:31 jakebice5991
You draw a card from a deck. if you get a red card, you win nothing. if you got a spade, you win $5. for any club, you win $10 plus an extra $20 for the ace of clubs. define random variable x as the amount you win at one game. a) what is the pmf of x? b) find expected value and standard deviation of x.
Answers: 2
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![E[X]=\displaystyle\sum_xxP(X=x)=\frac02+\frac54+\frac{10\cdot3}{13}+\frac{30}{52}=\frac{215}{52}](/tpl/images/0415/6538/47d1a.png)
![\mathrm{Var}[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2](/tpl/images/0415/6538/14d23.png)
![E[X^2]=\displaystyle\sum_xx^2P(X=x)=\frac{0^2}2+\frac{5^2}4+\frac{10^2\cdot3}{13}+\frac{30^2}{52}=\frac{2425}{52}](/tpl/images/0415/6538/34512.png)
![\mathrm{Var}[X]=\dfrac{2425}{52}-\left(\dfrac{215}{52}\right)^2=\dfrac{79875}{2704}](/tpl/images/0415/6538/3b499.png)
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You draw a card from a deck. if you get a red card, you win nothing. if you got a spade, you win $5....
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