Let a random variable is uniformly distributed over $[a,b]$ with expectation and variance $9.5$ and $1281$ respectively. Find the value of $ab$.

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$f(x)$=${kx_{2}0if x ∈ [0,1]otherwise$

Find $P(0.2<X<0.8)$?

Hint: $∫_{a}cx_{2}dx=c3b_{3}−a_{3}$ where, $c$ is a constant.

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$f(x)=⎩⎨⎧0.2x0.20.2x−0.20.40if 0≤x≤1if 1≤x≤2if 2≤x≤3if 3≤x≤4otherwise$

Find the probability that $0<x<2.5$. (Answer upto three decimal points)

Hint : Try to find the area under pdf using integration, otherwise draw the graph of pdf of $X$.

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$f(x)$=$⎩⎨⎧91e_{9−x}0if x > 0otherwise$

Find the probability that time between calls exceeds the mean time.

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