Science:Math Exam Resources/Courses/MATH105/April 2011/Question 09 (f)
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Question 09 (f) 

Each of the shortanswer questions below is worth 5 points. Put your answer in the box provided and show your work. No credit will be given for the answer without the correct accompanying work. A discrete random variable takes only two values, and Find if the variance of is 
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Hint 

The variance for a discrete random variable is defined to be where the values , are the possible outcomes for the random variable and is the mean: 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The variance for a discrete random variable is defined to be where the values , are the possible outcomes for the random variable and is the mean: In this case, there are only two possible outcomes or . If we define the probability with then by the law that the sum of the probabilities for all events must sum to one, we know that . Thus, Now we can use the definition of variance and get an equation for . Thus, the value of such that Var(X) = 1/4 is . 