###### GATE 2023

October 4, 2023###### NIC-NIELIT STA 2020

October 4, 2023# GATE 2016 [Set-1]

Question 14 |

A probability density function on the interval [*a,1*] is given by *1/x ^{2}* and outside this interval the value of the function is zero. The value of

*a*is _________.

0.7 | |

0.6 | |

0.5 | |

0.8 |

Question 14 Explanation:

The property of probability density function is area under curve = 1

or

where (a, b) is internal and f(x) is probability density function.

Given,

f(x) = 1/x

The area under curve,

– 1 + 1/a = 1

1/a = 2

a = 0.5

or

where (a, b) is internal and f(x) is probability density function.

Given,

f(x) = 1/x

^{2}, a≤x≤1The area under curve,

– 1 + 1/a = 1

1/a = 2

a = 0.5

Correct Answer: C

Question 14 Explanation:

The property of probability density function is area under curve = 1

or

where (a, b) is internal and f(x) is probability density function.

Given,

f(x) = 1/x

The area under curve,

– 1 + 1/a = 1

1/a = 2

a = 0.5

or

where (a, b) is internal and f(x) is probability density function.

Given,

f(x) = 1/x

^{2}, a≤x≤1The area under curve,

– 1 + 1/a = 1

1/a = 2

a = 0.5

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