Homework #2 ECES490-D Winter 2002Homework #2 ECES490-D Winter 2002 1. On planet Vulcan, there are 4 billion adults (men and women) and 5 billion children (boys and girls).Among adults, there are 3 billion men and there are 1 billion women. Among children, there are four billion boys and there are 1 billion girls. Children have heights uniformly distributed from 6”-12” (children instantly grow to their adult height when they turn into adults at age 75). Men’s heights are uniformly distributed between 18” and 36”. Women’sheights are uniformly distributed between 54” and 72”.On Vulcan, even if you know a person’s name, you cannot tell whether that person is a male (a boy or a man) or a female (a girl or a woman) unless you have more information. Boys are male Vulcans, and they become men when they turn into adults. Girls are female Vulcans, and the become women when they turn into adults. Boys are more likely than girls to kill each other in various war-like rituals... which is why the ratio of boys to girls is larger than the ratio of men to women. A Vulcan creates a message containing the following self-descriptive information about him or her:Message to be communicated:Name:Sex:Age:Height:When this message is received, at a distant location, it is not completely readable (due to impairments that are introduced in the communication process).You are trying to build a machine that uses the received message to estimate the height ofthe Vulcan who created the transmitted message, using mean squared error as the criterion for the goodness of the estimate. What are the minimum-mean-square-error estimators* for the following cases?A. The received message is completely readableB. Only the field with a name of the Vulcan is readableC. Only the field with the age of the Vulcan is readableD. Only the field with the sex of the Vulcan is readable*The estimator is the algorithm that specifies how to translate the received information into an estimate of the Vulcan’s height. For example, in case C. the estimator has the formIf the number in the age field is <75, then the minimum mean square error estimate is …If the number in the age field is >75, then the minimum mean square error estimate is …If the number in the age field is 75, then the minimum mean square error estimate is …Your answers to C and D must take into account the underlined text above. If your answers to C and D don’t take this into account, then they are not the right answers. To receive credit, your answers to C and D must take into account the underlined text
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