4. Suppose you are required to predict the value of the r.v. X. Assume that you know the distribution of X as well as the mean µ and variance σ². Suppose your prediction is a real number 0. The squared error (X – 0)² will be deducted from your paycheck. - (a) If your prediction is 0 = 2 and X turns out to be 7, what is your squared error? (b) If your prediction is 0 = 3/4 and X has a Bernoulli distribution with mean 1/3, what is your mean squared error? That is, compute E[(X - 0)²]. (c) If X has a uniform-(0, 1) distribution and your prediction is 0 = 1/3, what is your mean squared error?
4. Suppose you are required to predict the value of the r.v. X. Assume that you know the distribution of X as well as the mean µ and variance σ². Suppose your prediction is a real number 0. The squared error (X – 0)² will be deducted from your paycheck. - (a) If your prediction is 0 = 2 and X turns out to be 7, what is your squared error? (b) If your prediction is 0 = 3/4 and X has a Bernoulli distribution with mean 1/3, what is your mean squared error? That is, compute E[(X - 0)²]. (c) If X has a uniform-(0, 1) distribution and your prediction is 0 = 1/3, what is your mean squared error?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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