Please answer q's c and dLet p=6, q=7, m=0.67, let the first random variable be labelled E, and the second r.v. A. Let p be the largest digit in your student ID number. Let q be the number of non-zero digits inyour student ID number. Label the first random variable below using the first vowel in yourpreferred name throughout (e.g. in all expectations). Label the second (transformed) variableY in (e) using the first vowel in your family name. The the first vowels are the same, use, e.g.A₁ and A₂. Let m be a 2-digit decimal number using p and q as follows: m = 0.pq, i.e. p as thefirst digit, and q as the second.e.g. a student named John Randal with ID number 300012345 would have: Р 5, q 6, m = 0.56,would label the first random variable O, and the second A. A second student Luke Chu with ID number300101018 would have: p = 8, q = 5, m = 0.85, would label the first random variable U₁ and thesecond U₂.A continuous random variable has cdf03- {c++ 2² +2²=F(x)x < 0k(x+x²+x¹⁰) 0 1— (c) Sketch F(x) and indicate the value of x that satisfies F(x) = m [NB: only the basic propertiesof F(x) need to be correct, i.e. upper and lower limits, monotonicity.]. What name would begiven to this value of x? You do NOT need to calculate the solution.(d) Consider transforming the first variable using the function g(x) = q + xª. Find the cdf ofthis transformed variable, and indicate how the pdf would be found. Do NOT calculatethe pdf.

Answered: et p be the largest digit in your…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Please answer q's c and d

Let p=6, q=7, m=0.67, let the first random variable be labelled E, and the second r.v. A.

Let p be the largest digit in your student ID number. Let q be the number of non-zero digits in
your student ID number. Label the first random variable below using the first vowel in your
preferred name throughout (e.g. in all expectations). Label the second (transformed) variable
Y in (e) using the first vowel in your family name. The the first vowels are the same, use, e.g.
A₁ and A₂. Let m be a 2-digit decimal number using p and q as follows: m = 0.pq, i.e. p as the
first digit, and q as the second.
e.g. a student named John Randal with ID number 300012345 would have: Р 5, q 6, m = 0.56,
would label the first random variable O, and the second A. A second student Luke Chu with ID number
300101018 would have: p = 8, q = 5, m = 0.85, would label the first random variable U₁ and the
second U₂.
A continuous random variable has cdf
0
3- {c++ 2² +2²
=
F(x)
x < 0
k(x+x²+x¹⁰) 0<x<1
x > 1
—

(c) Sketch F(x) and indicate the value of x that satisfies F(x) = m [NB: only the basic properties
of F(x) need to be correct, i.e. upper and lower limits, monotonicity.]. What name would be
given to this value of x? You do NOT need to calculate the solution.
(d) Consider transforming the first variable using the function g(x) = q + xª. Find the cdf of
this transformed variable, and indicate how the pdf would be found. Do NOT calculate
the pdf.

Expert Solution

Step 1

Here, in the question it is given that number $m$ is written as $m = 0 . p q$ . Given the $F (x)$ in the question and it is asked to solve the question correctly. We have to indicate the value of $x$ that satisfies $f (x) = m$ . Also we have to name the value of $x$ . Consider transforming the first variable using the function. We have to find the cdf of this transformed variable and indicate how pdf would be found.

CDF is the cumulative distribution function where we find the sum of the values in range and about the whole range. The cumulative distribution function (cdf), which is frequently abbreviated as $F (x)$ , provides the likelihood that the random variable $X$ is less than or equal to $X$ . The function defined by $F (x) = P [X x]$ is the cumulative distribution function of the random variable $X$ .