My Math Forum Function Of Discrete Random Variable

 April 8th, 2018, 06:31 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 06:35 PM.
April 8th, 2018, 06:59 PM   #2
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Quote:
 Originally Posted by Shima 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?
Assuming we have a fair coin the number of heads that appear

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 $k$

$v[k] = 2k-8$

$P[\text{we lose money}] = P[k < 4] = p[0]+p[1]+p[2]+p[3] = \dfrac{11}{64}$

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