InterviewSolution
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InterviewSolution
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If a curve X has probability density function (pdf) `f(x)={{:(ax","0lexle1),(a","1lexle2),(3a-ax","2lexle3),(0",""otherewise"):}` Then, a is equal toA. 1B. `1/3`C. `1/2`D. `1/5` |
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Answer» Correct Answer - C `therefore f(x)` is a pdf `therefore" "oversetoounderset(-oo)intf(x)dx=1rArroverset3underset0intf(x)=1` `rArr" "overset1underset0intf(x)dx+overset2underset1intf(x)dx+overset3underset2intf(x)dx=1` `rArr" "overset1underset0int(ax)dx+overset2underset1int(a)dx+overset3underset2int(3a-ax)dx=1` `rArr" "a[x^2/2]_0^1+a[x]_1^2+a[3x-x^2/2]_2^3=1` `rArr" "a/2+a+a{(9-9/2)-(6-2)}=1` `therefore" "2a=1` `rArr" "a=1/2` |
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