a) X has standard deviation ox = 10 and P[X < 10] = 0.933. Find its mean ux. b) Y has standard deviation ơy 10 and P[Y < 0] = 0.067. Find its mean µy. c) It is known that P[Z < 10] = 0.977. Express its mean uz in terms of its standard deviation oz. d) It is known that P[W > 12] = 1/2. but its standard deviation is unknown, Can vou

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The following random variables X, Y, Z, W are known to be Gaussian.

 

a) X has standard deviation ox =
10 and P[X < 10] = 0.933. Find its mean µx.
b) Y has standard deviation ơy =
10 and P[Y 0] = 0.067. Find its mean Hy.
c) It is known that P[Z < 10] = 0.977. Express its mean uz in terms of its standard
deviation oz.
d) It is known that P[W > 12] = 1/2, but its standard deviation is unknown. Can you
find uw?
Transcribed Image Text:a) X has standard deviation ox = 10 and P[X < 10] = 0.933. Find its mean µx. b) Y has standard deviation ơy = 10 and P[Y 0] = 0.067. Find its mean Hy. c) It is known that P[Z < 10] = 0.977. Express its mean uz in terms of its standard deviation oz. d) It is known that P[W > 12] = 1/2, but its standard deviation is unknown. Can you find uw?
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