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Let the random variable X is defined as ...

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 bell

Text Solution

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Required probability = `P(X gt 1.5)=underset(1.5)overset(oo)int f(x)dx`
` = underset(1.5)overset(2)intf(x)dx = k underset(1.5)overset(2)intx^(2) dx`
`- k[(x^(3))/(3)]_(1.5)^(2) = (k)/(3)[x^(3)]_(1.5)^(2)`
`=(k)/(3)[ 8- 3.375]=(1)/(3) xx(3)/(8)xx 4.625`
`= 0.578`
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