Q2/A/ Two random variables X and Y with joint probability distribution given by: 2x + 2y f(x,y) = for x = 0,1,2,3,4 y = 0,1,2 60 Calculate: (a) P(X>Y); (b) P(X>2, Y

Q2/A/ Two random variables X and Y with joint probability distribution given by:<br>2x + 2y<br>f(x,y) =<br>for x = 0,1,2,3,4 y = 0,1,2<br>60<br>Calculate:<br>(a) P(X>Y);<br>(b) P(X>2, Y < 2);<br>(c) P (X < 3, Y = 2);<br>(d) P (X + Y = 3).<br>Q2/B/ Two random variables X and Y with joint density function given by:<br>1<br>3 (2x + 4y)<br>0 < x, y < 1<br>f(x, y) =<br>elsewhere<br>(a) Find the marginal density of Y.<br>(b) Find the marginal density of X.<br>(c) Find P(x < 1/3)<br>Q3/ consider a random variable<br>with density function<br>0.125(4 + 2x)<br>1< x < 2<br>{<br>f(x) =<br>elsewhere<br>Find the variance for g(X) = 4x² + 3<br>

Extracted text: Q2/A/ Two random variables X and Y with joint probability distribution given by: 2x + 2y f(x,y) = for x = 0,1,2,3,4 y = 0,1,2 60 Calculate: (a) P(X>Y); (b) P(X>2, Y < 2);="" (c)="" p="" (x="">< 3,="" y="2);" (d)="" p="" (x="" +="" y="3)." q2/b/="" two="" random="" variables="" x="" and="" y="" with="" joint="" density="" function="" given="" by:="" 1="" 3="" (2x="" +="" 4y)="" 0="">< x,="" y="">< 1="" f(x,="" y)="elsewhere" (a)="" find="" the="" marginal="" density="" of="" y.="" (b)="" find="" the="" marginal="" density="" of="" x.="" (c)="" find="" p(x="">< 1/3)="" q3/="" consider="" a="" random="" variable="" with="" density="" function="" 0.125(4="" +="" 2x)="">< x="">< 2="" {="" f(x)="elsewhere" find="" the="" variance="" for="" g(x)="4x²" +="">

Jun 04, 2022

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Q2/A/ Two random variables X and Y with joint probability distribution given by: 2x + 2y f(x,y) = for x = 0,1,2,3,4 y = 0,1,2 60 Calculate: (a) P(X>Y); (b) P(X>2, Y

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