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Chapter 5: Q. 5.16 (page 215)

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

Short Answer

Expert verified

It's up to 1a-xif xin (0,a)otherwise its adequate iszero.

Step by step solution

01

Find the Variable function.

The hazard rate of the random variable is that the function

位(x)=f(x)1-F(x)

for every XspecifiedF(x)<1otherwise it's capable of zero.

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

F(x)=xa

02

Equation of hazard rate.

forx鈭�(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-xa=a-xa

Finally, the hazard rate is adequate

位(x)=1aa-xa=1a-x

For x鈭�(0,a)

Otherwise, it's up to zero.

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Most popular questions from this chapter

If has a hazard rate function位X(t), compute the hazard rate function of aXwhere ais a positive constant.

An image is partitioned into two regions, one white and the other black. A reading taken from a randomly chosen point in the white section will be normally distributed with 渭=4and 蟽2=4, whereas one taken from a randomly chosen point in the black region will have a normally distributed reading with parameters (6,9). A point is randomly chosen on the image and has a reading of 5. If the fraction of the image that is black is 伪, for what value of 伪would the probability of making an error be the same, regardless of whether one concluded that the point was in the black region or in the white region?

If xis uniformly distributed over (a,b), what random variable, having a linear relation with x, is uniformly distributed over (0,1)?

The random variable X is said to be a discrete uniform random variable on the integers 1, 2, . . . , n if P{X = i } = 1 n i = 1, 2, . . , n For any nonnegative real number x, let In t(x) (sometimes written as [x]) be the largest integer that is less than or equal to x. Show that if U is a uniform random variable on (0, 1), then X = In t (n U) + 1 is a discrete uniform random variable on 1, . . . , n.

The standard deviation of X, denoted SD(X), is given by

SD(X)=Var(X)

Find SD(aX+b) if X has variance 蟽2.
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