A finite set of random variables X having upto 100 elements; $X = {x_{1}, x_{2}, . . . . . . x_{100}}$ is uniformly distributed over an interval of [0, 1] and are independent of each other. The probability that x100 is the largest i.e., $P (x_{100} i s l a r g e s t) i s$ ________
0.01

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Solution

The correct option is A 0.01

$P (x_{100} i s l a r g e s t) = \int_{0}^{1} k^{99} d k = \frac{1}{100} = 0.01$

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A finite set of random variables X having upto 100 elements; X={x1,x2,......x100} is uniformly distributed over an interval of [0, 1] and are independent of each other. The probability that x100 is the largest i.e., P(x100 is largest) is ________0.01

The correct option is A 0.01 P(x100 is largest)=∫10k99dk=1100=0.01

A finite set of random variables X having upto 100 elements; $X = {x_{1}, x_{2}, . . . . . . x_{100}}$ is uniformly distributed over an interval of [0, 1] and are independent of each other. The probability that x100 is the largest i.e., $P (x_{100} i s l a r g e s t) i s$ ________
0.01

The correct option is A 0.01

$P (x_{100} i s l a r g e s t) = \int_{0}^{1} k^{99} d k = \frac{1}{100} = 0.01$