O Course Modules: 2017F- × / \"A HW3 STAT 201: RVs and x \'\\ e che99 Study | Gu
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O Course Modules: 2017F- × / "A HW3 STAT 201: RVs and x ' e che99 Study | Guided S × eHW3 STAT 201 RVs A C www.webassign.net/web/Student Assignment-Responses/submit?dep-17194071 B. wnaris tne prooaDty tnartne arcuris Still Tunctiona at tne ena or tne time perioar Uygg3 3. -/7 points My Notes Ask Your Let the random variable X represent the number of girls in a family of three children. Fill in the table below that represents the probability distribution for X Hint: Either write out the sample space for this problem like we did with the coin flipping example, or model X with a Binomial distribution and do the computations using f(x) 0 (a) What is the probability of having at least 1 girl in a family of 3 children? (b) What is the mean of the distribution? (c) What is the standard deviation of the distribution? Submit Assignment Save Assignment Progress Home My Assignments Extension Request webAss°18 4 0 1997-2017 Advanced Instructional Systems, Inc Al rights reserved. O Type here to search 9/17/2017Explanation / Answer
P(girl), p = 0.5
n = 3
f(X = 0) = 3C0 * 0.50 * 0.53 = 0.125
f(X = 1) = 3C1 * 0.51 * 0.52 = 0.375
f(X = 2) = 3C2 * 0.52 * 0.51 = 0.375
f(X = 3) = 3C3 * 0.53 * 0.50 = 0.125
A) P(X > 1) = 1 - P(X = 0) = 1 - 0.125 = 0.875
B) mean = n * p = 3 * 0.5 = 1.5
C) standard deviation = sqrt(n*p*(1-p)) = sqrt(3*0.5*0.5) = 0.866
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