Chapter 5: Q. 5.16 (page 215)

Compute the hazard rate function of $X$ when $X$ is uniformly distributed over. $(0, a)$

Short Answer

Expert verified

It's up to $\frac{1}{a - x}$ if $x$ in $(0, a)$ otherwise its adequate iszero.

Step by step solution

Find the Variable function.

The hazard rate of the random variable is that the function

$λ (x) = \frac{f (x)}{1 - F (x)}$

for every $X$ specified $F (x) < 1$ otherwise it's capable of zero.

We know that the CDF of Uniform distribution over $(0, a)$

$F (x) = \frac{x}{a}$

Equation of hazard rate.

for $x \in (0, a)$ left from that interval it's capable of zero, right from that interval is an adequate one.

Hence, we have got that

$1 - F (x) = 1 - \frac{x}{a} = \frac{a - x}{a}$

Finally, the hazard rate is adequate

$λ (x) = \frac{\frac{1}{a}}{\frac{a - x}{a}} = \frac{1}{a - x}$

For $x \in (0, a)$

Otherwise, it's up to zero.

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Compute the hazard rate function of $X$ when $X$ is uniformly distributed over. $(0, a)$

Short Answer

Step by step solution

Find the Variable function.

Equation of hazard rate.

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Compute the hazard rate function of Xwhen Xis uniformly distributed over.(0,a)

Short Answer

Step by step solution

Find the Variable function.

Equation of hazard rate.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Theoretical and Mathematical Physics

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Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Compute the hazard rate function of $X$ when $X$ is uniformly distributed over. $(0, a)$