(i) Attempt the following questions. Show all necessary steps. Read the questions carefully. (ii) Any copied material from internet or your class fellows will get you ZERO marks. Q. 1 Let X be the...


(i) Attempt the following questions. Show all necessary steps. Read<br>the questions carefully. (ii) Any copied material from internet or<br>your class fellows will get you ZERO marks.<br>Q. 1 Let X be the number of bugs in the first draft of a piece of software,<br>and let Y be the number of bugs remaining in the second draft of the same<br>software. Their joint probability mass function is given by the following<br>table:<br>Y<br>0.<br>1<br>3<br>0.<br>0.03<br>0.14<br>0.09<br>0.08<br>1<br>0.05<br>0.10<br>K<br>0.04<br>0.04<br>0.09<br>0.08<br>0.09<br>(i) Obtain K so that it is the joint probability mass function;<br>(ii) Find cumulative distribution function Fyy (x, y);<br>(iii) Find the following probabilities using cdf obtained above (a) P(X <<br>3, Y < 2), (b) P(XY > 4), (c) P(X + Y > 3), (e) P(X < 3,Y < 2)<br>21<br>

Extracted text: (i) Attempt the following questions. Show all necessary steps. Read the questions carefully. (ii) Any copied material from internet or your class fellows will get you ZERO marks. Q. 1 Let X be the number of bugs in the first draft of a piece of software, and let Y be the number of bugs remaining in the second draft of the same software. Their joint probability mass function is given by the following table: Y 0. 1 3 0. 0.03 0.14 0.09 0.08 1 0.05 0.10 K 0.04 0.04 0.09 0.08 0.09 (i) Obtain K so that it is the joint probability mass function; (ii) Find cumulative distribution function Fyy (x, y); (iii) Find the following probabilities using cdf obtained above (a) P(X < 3,="" y="">< 2),="" (b)="" p(xy=""> 4), (c) P(X + Y > 3), (e) P(X < 3,y="">< 2)="">

Jun 09, 2022
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