InterviewSolution
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InterviewSolution
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Let the random variable X is defined as time (in minutes) that elapses between the bell and end of the lecture in case of collagen professor whrer pdf is defined as `f(x)={{:(kx^2","0lexlt2),(0", ""elsewhere"):}` find the probability that lecture continue for atleast 90s beyond the bellA. `(37)/(64)`B. `(35)/(64)`C. `(33)/(69)`D. None of these |
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Answer» Correct Answer - A We known that `oversetoounderset(-oo)intf(x)dx=1` `therefore" "0+underset0overset2intf(x)dx=1` `rArr" "underset0overset2intkx^2dx=1` `rArr" "k[x^3/3]_0^2=1rArr[8/3]=1` `rArr" "k=3/8` Clearly, the probability that the lecture continuous for at least 90s i.e.`3/2` min beyond the bell `=P(3/2lexle2)=overset2underset(3//2)intf(x)dx=k""overset2underset(3//2)intx^2dx` `=k[x^3/3]_(3//2)^2=k/3[8-(27)/8]=(37k)/(24)` `=(37xx3/8)/(24)=(37)/(64)` |
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