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Question

Let Y be a continuous random variable whose PDF is as g(y)=y4125 for yϵ(0,a). Constant "a" makes g(y) a valid PDF. Find the value of a5.

A
225
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B
625
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C
525
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D
None of these
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Solution

The correct option is B 625
Let Y be a continuous random variable whose PDF is as g(y)=y4125 for y(0,a).
Also given that constant a makes g(y) a valid PDF.
We have to find the value of a5.
We know that, a PDF is valid if it satisfies the following
(1) f(x) is positive everywhere.

(2) The area under the curve f(x) in the range (a,b)is 1, that is: baf(x)dx=1.

Thus we have a0g(y)dy=1

a0y4125dy=1

1125a0y4dy=1

1125[y55]a0=1

1625[y5]a0=1

1625[a50]=1

a5625=1

a5=625


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