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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> A fair coin is tossed three times. Let <math>X</math> be the number of heads that turn up on the first two tosses and <math>Y</math> the number of heads that turn up on the third toss. Give the distribution of <ul><li> the random variables <math...") |
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A fair coin is tossed three times. Let <math>X</math> be the number of heads that turn up on the first two tosses and <math>Y</math> the number of heads that turn up on the third toss. | |||
turn up on the first two tosses and <math>Y</math> the number of heads that turn up on the third toss. | |||
Give the distribution of | Give the distribution of | ||
<ul><li> the random variables <math>X</math> and <math>Y</math>. | <ul style="list-style-type:lower-alpha"><li> the random variables <math>X</math> and <math>Y</math>. | ||
</li> | </li> | ||
<li> the random variable <math>Z = X + Y</math>. | <li> the random variable <math>Z = X + Y</math>. | ||
Latest revision as of 17:11, 19 June 2024
A fair coin is tossed three times. Let [math]X[/math] be the number of heads that turn up on the first two tosses and [math]Y[/math] the number of heads that turn up on the third toss.
Give the distribution of
- the random variables [math]X[/math] and [math]Y[/math].
- the random variable [math]Z = X + Y[/math].
- the random variable [math]W = X - Y[/math].