a. Obtain the cdf of X.b. What is P(X ≤ .5)?c. Using the cdf from (a), what is P(.25 < X ≤ .5)?d. What is the 75th percentile of the distribution? When we say that an individual's test score was at the 85th percentile of thepopulation, we mean that 85% of all population scores were below that score and15% were above. Let's define percentile formally.Let p be a number between 0 and 1. The (100p)th percentile of the distribu-tion of a continuous rv X, denoted by n(p), is defined byp = F(n(p)) = | f(y) dy.The median of a continuous distribution, denoted by u, is the 50th percentile.2. Let X denote the amount of space occupied by an item from Amazon placedin a 1-ft packing container. The pdf of X is[ 90x°(1 – x),f(x) =| 0,0 < x < 1otherwise

we have the pdf, f(x) = 90x8(1-x)= 90(x8-x9) for 0<x<1 we want to find, a. Obtain the cdf of…

Answered: a. Obtain the cdf of X. b. What is P(X…

a. Obtain the cdf of X. b. What is P(X ≤ .5)? c. Using the cdf from (a), what is P(.25 < X ≤ .5)? d. What is the 75th percentile of the distribution?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

a. Obtain the cdf of X.

b. What is P(X ≤ .5)?

c. Using the cdf from (a), what is P(.25 < X ≤ .5)?

d. What is the 75th percentile of the distribution?

When we say that an individual's test score was at the 85th percentile of the
population, we mean that 85% of all population scores were below that score and
15% were above. Let's define percentile formally.
Let p be a number between 0 and 1. The (100p)th percentile of the distribu-
tion of a continuous rv X, denoted by n(p), is defined by
p = F(n(p)) = | f(y) dy.
The median of a continuous distribution, denoted by u, is the 50th percentile.
2. Let X denote the amount of space occupied by an item from Amazon placed
in a 1-ft packing container. The pdf of X is
[ 90x°(1 – x),
f(x) =
| 0,
0 < x < 1
otherwise

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