Ebru is an entrepreneur. She plans to start 2 different very small businesses in the next year. Both businesses are independent of each other, and each business has a 50% chance of being successful and a 50% chance of failing. Each business will make Ebru $200 if it succeeds or lose her $200 if it fails. if X is a random variable that represents Ebru's profit from starting these 2 businesses, drag the bars to graph the probability distribution for all possible values of X.
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Answer:
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Given : each business has a 50% chance of being successful and a 50% chance of failing. Each business will make Ebru $200 if it succeeds or lose her $200 if it fails.
X is a random variable that represents Ebru's profit from starting these 2 businesses
To Find : draw bars to graph the probability distribution for all possible values of X.
Solution:
if both business success then profit = 200 + 200 = 400
if both business fails then loss = 200 + 200 = 400 or
loss 400 = - 400 profit
if one succeeds and other fails then profit = 200 - 200 = 0
Probability of success = Probability of fail = 1/2
X P(X) XP(X)
400 (1/2)(1/2) = 1/4 100
0 (1/2)(1/2) + (1/2)(1/2) = 1/2 0
-400 (1/2)(1/2) = 1/4 -100
∑XP(X) = 0
Hence no expected loss or profit
bars to graph the probability distribution for all possible values of X. is attached
X P(X)
400 0.25
0 0.5
-400 0.25
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