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April 8th, 2018, 07:31 PM  #1 
Newbie Joined: Apr 2018 From: Canada Posts: 3 Thanks: 0  Function Of Discrete Random Variable
Suppose you are playing a game that costs 8 dollars to play. You flip 10 coins and, for every head, you win 2 dollars. Whats the probability you lose money?
Last edited by Shima; April 8th, 2018 at 07:35 PM. 
April 8th, 2018, 07:59 PM  #2  
Senior Member Joined: Sep 2015 From: USA Posts: 2,299 Thanks: 1218  Quote:
is a binomial random variable with probability mass function $p[k] = \dbinom{10}{k}\left(\dfrac 1 2\right)^{10} = \dfrac{\dbinom{10}{k}}{1024}$ we can then associate the earnings with each value of $k$ $v[k] = 2k8$ $P[\text{we lose money}] = P[k < 4] = p[0]+p[1]+p[2]+p[3] = \dfrac{11}{64}$  

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discrete, function, random, variable 
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