Turito Academy

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Given : <img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/1714932/1/910911/Picture3.png" alt="" width="337" height="67" /> Sum of all probabilities is 1 P(x=1) + P(x = 2) + P(x = 3) + P(x =4)  = 1 k + 2k + 3k + 4k = 1 k = <img src="data:image/png;base64,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" class="Wirisformula" alt="1 over 10" width="28" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»10«/mn»«/mfrac»«/math»'/> Now, P(x &lt; 3) = P(x=1) + P(x =3) P(x &lt; 3) = k + 2k = 3k = <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABwAAAAjCAYAAACHIWrsAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAARtJREFUeNpjYCAeOALxNiD+BsQ/gPgWEE8AYmEGGoH9QBwExGxIYgZAvIOBzuATPS1TAuIb9LBIHIgTofHoRUuL/qPhAnoFpSAQBwDxSSC2p2cc8kAtpSv4QU/L9KAJhybgIBCHAjELEDNBS577QBxPKwttgXgLNAh/QEseH4ZRMAroCf7TGI+CUUAboAbEtUB8AY8aPiCeBq0XQXgmVIwssBiI0wgk671A7IfE94GKUZxHsQFQdTUJiziogRxJCwvXALEbjlb6GlpY+A6tJQ4DILGXtLDwDx49v+ht4Q9aWPgSR5By0CpIQQnDA4u4G60SDaj7NhuL+HxaZQtYv7EA2nwEBW81tElJtUoZWz9jLjSRfIMWbTy4DAQA8KpcPj1YshQAAABjdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtbj4zPC9tbj48bW4+MTA8L21uPjwvbWZyYWM+PC9tYXRoPnzuDUkAAAAASUVORK5CYII=" class="Wirisformula" alt="3 over 10" width="28" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»3«/mn»«mn»10«/mn»«/mfrac»«/math»'/> Thus, the value of <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAANCAYAAACQN/8FAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIFJREFUeNpjYEAF34CYiYEAUAHiSwxEgAAgXk6MwnogLoeyWYB4IRB7YVO4CmoqB5TtiMvEW0CsA8SbgNgclyImqI+PQxXjBCAT9gNxJBDPxacQpGA+lN0DxBm4FE4C4jQk/m4gtsamcB1aUAgC8UkglkRX+A4aLMgA5Km9WMTxAwDPrRQqsprlpQAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+azwvbWk+PC9tYXRoPsjDLjEAAAAASUVORK5CYII=" class="Wirisformula" alt="k" width="10" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»k«/mi»«/math»'/>  is <img src="data:image/png;base64,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" class="Wirisformula" alt="1 over 10" width="28" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»10«/mn»«/mfrac»«/math»'/> and P(X&lt;3) is <img src="data:image/png;base64,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" class="Wirisformula" alt="3 over 10" width="28" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»3«/mn»«mn»10«/mn»«/mfrac»«/math»'/>

A random variable X has the following distribution <img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/1714932/1/910911/Picture3.png" alt="" width="337" height="67" /> The value of <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAANCAYAAACQN/8FAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIFJREFUeNpjYEAF34CYiYEAUAHiSwxEgAAgXk6MwnogLoeyWYB4IRB7YVO4CmoqB5TtiMvEW0CsA8SbgNgclyImqI+PQxXjBCAT9gNxJBDPxacQpGA+lN0DxBm4FE4C4jQk/m4gtsamcB1aUAgC8UkglkRX+A4aLMgA5Km9WMTxAwDPrRQqsprlpQAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+azwvbWk+PC9tYXRoPsjDLjEAAAAASUVORK5CYII=" class="Wirisformula" alt="k" width="10" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»k«/mi»«/math»'/> and P(X&lt;3) are equal to

Solution for the question - a random variable x has the following distribution the value of and p(x k=(1)/(24),p(x k=(3)/(10),p(x