exercise:00980bf1cb: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> Following Galton, let us assume that the fathers and sons have heights that are dependent normal random variables. Assume that the average height is 68 inches, standard deviation is 2.7 inches, and the correlation coefficient is .5 (see Exercises...") |
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Following Galton, let us assume that the fathers and sons have heights that are dependent normal random variables. Assume that the average | |||
have heights that are dependent normal random variables. Assume that the average | |||
height is 68 inches, standard deviation is 2.7 inches, and the correlation coefficient | height is 68 inches, standard deviation is 2.7 inches, and the correlation coefficient | ||
is .5 (see Exercises [[exercise:Bf1fbb9234 |Exercise]] and [[exercise:Cc5799edfb |Exercise]]). That is, assume that | is .5 (see Exercises [[exercise:Bf1fbb9234 |Exercise]] and [[exercise:Cc5799edfb |Exercise]]). That is, assume that | ||
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respectively, where <math>X</math> and <math>Y</math> are correlated standardized normal random variables, | respectively, where <math>X</math> and <math>Y</math> are correlated standardized normal random variables, | ||
with correlation coefficient .5. | with correlation coefficient .5. | ||
<ul><li> What is the expected height for the son of a father whose height is 72 inches? | <ul style="list-style-type:lower-alpha"><li> What is the expected height for the son of a father whose height is 72 inches? | ||
</li> | </li> | ||
<li> Plot a scatter diagram of the heights of 1000 father and son pairs. '' Hint'': You can choose standardized pairs as in | <li> Plot a scatter diagram of the heights of 1000 father and son pairs. '' Hint'': You can choose standardized pairs as in [[exercise:F25f83f07c |Exercise]] and then | ||
plot <math>(2.7X + 68, 2.7Y + 68)</math>. | plot <math>(2.7X + 68, 2.7Y + 68)</math>. | ||
</li> | </li> | ||
</ul> | </ul> | ||
Latest revision as of 21:50, 14 June 2024
Following Galton, let us assume that the fathers and sons have heights that are dependent normal random variables. Assume that the average height is 68 inches, standard deviation is 2.7 inches, and the correlation coefficient is .5 (see Exercises Exercise and Exercise). That is, assume that the heights of the fathers and sons have the form [math]2.7X + 68[/math] and [math]2.7Y + 68[/math], respectively, where [math]X[/math] and [math]Y[/math] are correlated standardized normal random variables, with correlation coefficient .5.
- What is the expected height for the son of a father whose height is 72 inches?
- Plot a scatter diagram of the heights of 1000 father and son pairs. Hint: You can choose standardized pairs as in Exercise and then plot [math](2.7X + 68, 2.7Y + 68)[/math].