Let X be the temperature in °C at which a certain chemical reaction takes place, and let Y be the temperature in °F (so Y = 1.8X + 32).(a) If the median of the X distribution is p, show that 1.8 + 32 is the median of the Y distribution.P(Y s 1.8ũ + 32)= PY< 1.8 + 32= PSince i is the median of X, P(X sP) =0.50.5. Thus, 1.8ũ + 32 is the median of Y.(b) How is the 90th percentile of the Y distribution related to the 90th percentile of the X distribution?ny(.9) = ( 1.8n,(.9) + ( 32Verify your conjecture.P(Y s 1.87(.9) + 32)<1.87 .9) + 32= PlX

Here X is the temperature in 0C , and let Y be a the temperature in 0F, thus Y=1.8X+32 a.) If the…

Let X be the temperature in °C at which a certain chemical reaction takes place, and let Y be the temperature in °F (so Y = 1.8X + 32). (a) If the median of the X distribution is p, show that 1.8 + 32 is the median of the Y distribution. P(Y s 1.8ũ + 32) = PY S 1.8 + 32 = P X Since i is the median of X, P(X s p) = 0.5 0.5. Thus, 1.8 + 32 is the median of Y. (b) How is the 9oth percentile of the Y distribution related to the 90th percentile of the X distribution? n,(.9) = ( 1.8 + Verify your conjecture. P(Y s 1.8n(.9) + 32) = P 1 S 1.8n 1.9) + 32 (16% 5 Since n1.9) is the 90th percentile of X, P(X s n.9)) = 0.9 X . Thus, 1.87 4.9) + 32 is the 90th percentile of Y. (c) More generally, if Y = ax + b, how is any particular percentile of the Y distribution related to the rresponding percentile of the X distribution? ndo) - ( 32 1.8 This is a result of the following. P(Y s an Ap) + b) P Y s anlp) + b) = P Since n (p) is the (100p)th percentile of X, P(X s n (p)) = p. Thus, an (p) + b is the (100p)th percentile of Y.

Let X be the temperature in °C at which a certain chemical reaction takes place, and let Y be the temperature in °F (so Y = 1.8X + 32). (a) If the median of the X distribution is p, show that 1.8 + 32 is the median of the Y distribution. P(Y s 1.8ũ + 32) = PY S 1.8 + 32 = P X Since i is the median of X, P(X s p) = 0.5 0.5. Thus, 1.8 + 32 is the median of Y. (b) How is the 9oth percentile of the Y distribution related to the 90th percentile of the X distribution? n,(.9) = ( 1.8 + Verify your conjecture. P(Y s 1.8n(.9) + 32) = P 1 S 1.8n 1.9) + 32 (16% 5 Since n1.9) is the 90th percentile of X, P(X s n.9)) = 0.9 X . Thus, 1.87 4.9) + 32 is the 90th percentile of Y. (c) More generally, if Y = ax + b, how is any particular percentile of the Y distribution related to the rresponding percentile of the X distribution? ndo) - ( 32 1.8 This is a result of the following. P(Y s an Ap) + b) P Y s anlp) + b) = P Since n (p) is the (100p)th percentile of X, P(X s n (p)) = p. Thus, an (p) + b is the (100p)th percentile of Y.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: distribution is given as X ~ U(0, 12). Find P(x > 3)

Q: Frequency. 305 316 299 281 Season tarcher dans that the numbe of homicide crimes by season is…

A: The claim of the test is that the number of homicide crimes by season is uniformly distributed. The…

Q: Q3- A- Find the critical (t) values for: 1- a= 0.01 with d.f. = 15 for a right-tailed t test. 2- a=…

Q: Interpret the slope coefficients that you deemed significant in the expected direction. Does the…

A: Regression equation comprising more than one factor is called multiple regression equation.

Q: (d) Find the (cumulative) distribution function for X, Fx(x). (e) Using the distribution function,…

Q: For a 10-year term insurance of 1000 on (x), you are given: i. The death benefit is payable at the…

Q: 1. You have the following PDF: f(x) = {1/9 1 ≤ x ≤ 10} (e) Calculate P(2 < X < 5). (f) Calculate P(X…

A: Given;PDF of X is :f(x)=19 ; 1≤x≤10

Q: F(12,6). Find the following: (a ) F0.05 (12,6). (b) F0.95 (12,6). (c ) P(0.33 ≤ W≤ 4.00).

A: (12,6)=1/F0.05(6,12)=1/3=0.33Given that W ~F(12,6)where r1=12 and r2=6 a) F0.05(12,6) is given in…

Q: A distribution is given as X ~ U(0, 15). Find P(x < 4) and round to the nearest hundredths place.…

A: It is given that the X~U(0,15).

Q: For constants o > 0 and a > 0, the function aoª p(x) xa+1> where x > 0, is called a Pareto…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…

Q: At a particular fast-food restaurant, food is often made in advance, and then it is placed under a…

A: The given function

Q: A random sample of size n =5 is taken from a lognormal distribution with parameters u = 0.7 and o…

A: Hey there! Thank you for posting the question. Since there are multiple questions posted, we will…

Q: find z such that 5.2% of the standard curve lies to the left of z.

A: Probability = 0.052 Finding the value of z corresponding to p=0.052= -1.62576 ( From Excel…

Q: 1.2. Assume that Billy's driving time to class is uniformly distributed from 15-20 minutes in good…

A: Given, Billy's driving time to class is uniformly distributed from 15-20 minutes in good weather,…

Q: Q5. The correlation coefficient will be zero when А. Е(X— X)(Y— Ў) —D 0 B. E(X – X)² = 0 С. | C. E(Y…

A: We know that. If r is equal to +1 then there are strong positively correlation and If r is equal to…

Q: Use the t-distribution to find P(-2.28 < t < 1.26). let n=22.

A: From the given information, The number of sample observations is n=22. The degree of freedom is, n…

Q: George plans to take simple random sample of size 50 from a population, and to compute the mean…

A: Given: The size of the sample is n=50. The population mean is μ=145. The population standard…

Q: x has the uniform distribution [0,1] put y=2x + 5 then y has the uniform distribution on the…

Q: Consider an individual who is risk-loving instead of risk-averse. a. Is U(I) concave or convex?b.…

A: a. If an individual is risk-loving, their utility function U(I) is likely to be convex, rather than…

Q: Suppose P(A) = P(B) = 0.2 and P(AN B) = 0.1. What is P(AU B)?

Q: For a 10-year term insurance of 1000 on (x), you are given: i. The death benefit is payable at the…

A: For a10-year term insurance of 1000 on (x), you are given.i) The death benefit is payable at the…

Q: 12) A metal bar is heated, and then allowed to cool. Its temperature T (in °C) is found to be The…

A: 12.) The temperature, T, at any time, t, is given as:T=15+75e−0.25tIt is required to find the rate…

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Let X be the temperature in °C at which a certain chemical reaction takes place, and let Y be the temperature in °F (so Y = 1.8X + 32).
(a) If the median of the X distribution is p, show that 1.8 + 32 is the median of the Y distribution.
P(Y s 1.8ũ + 32)
= P
Y
< 1.8 + 32
= P
Since i is the median of X, P(X sP) =
0.5
0.5. Thus, 1.8ũ + 32 is the median of Y.
(b) How is the 90th percentile of the Y distribution related to the 90th percentile of the X distribution?
ny(.9) = ( 1.8
n,(.9) + ( 32
Verify your conjecture.
P(Y s 1.87(.9) + 32)
<1.87 .9) + 32
= Pl
X
<ny(.9)
= P
Since n1.9) is the 90th percentile of X, P(X s n1.9)) = 0.9
. Thus, 1.8n 1.9) + 32 is the 90th percentile of Y.
(c) More generally, if Y = ax + b, how is any particular percentile of the Y distribution related to the corresponding percentile of the X distribution?
nAe) = (| 1.8
ndo) - (32
This is a result of the following.
P(Y s an Ap) + b) = P( Y
s anx(p) +
= P X
Since n (p) is the (100p)th percentile of X, P(X sn 0)) = p. Thus, an (p) + b is the (100p)th percentile of Y.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 43 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.50 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit 1 upper limit 2 margin of error 3 (b) What conditions are necessary for your calculations? (Select all that apply.) n is large the distribution of weights is normal σ is known the distribution of weights is uniform σ is unknown (c) Interpret your results in the context of this problem. 1% of the intervals created using…
Test a claim that the mean amount of carbon monoxide in the air in U.S. cities is less than 2.33 parts per million. It was found that the mean amount of carbon monoxide in the air for the random sample of 65 cities is 2.39 parts per million and the standard deviation is 2.09 parts per million. At a = 0.05, can the claim be supported? Complete parts (a) through (e) below. Assume the population is normally distributed. (a) Identify the claim and state H, and Ha. Which of the following correctly states H, and H,? Ho: = |2.33 Hạ: < 2.33 (Type integers or decimals. Do not round.) The claim is the alternative hypothesis. (b) Use technology to find the critical value(s) and identify the rejection region(s). The critical value(s) is/are to = (Use a comma to separate answers as needed. Round to two decimal places as needed.)
*2. Let log Y the median of Y). ~ N (u, o2). Find the distribution of Y and show that P(Y < eH) = 0.5 (i.e., el is
3x-2y For x =-1,0,1 and y = -1,0. The joint distribution of X and Y is given by: f(x.y) = For x = -1,0,1 and y = -1,0. Then k = None of these O 18 24 36
A fair 6-sided die is rolled, and then a coin with probability p of Heads is flipped as manytimes as the die roll says. (For example, if we roll a 3, then we flip the coin 3 times.) Let Xbe the result of the die roll and Y be the number of times the coin lands Heads.(a) Find the joint PMF of X and Y . Write the answer as a table (b) Find the marginal PMF of X.(c) Find the marginal PMF of Y .(d) Are X and Y independent? Why?(e) Find the conditional PMF of X given Y = 2.
Consider the curve below 0.2- 1 2 3 4 5 6 Find the probability that x < 2 P (x < 2) =