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Let𝛼(𝑥)=𝑥 and define𝑓 as𝑓(𝑥)=1 if𝑥 is rational and𝑓(𝑥)=0 if𝑥 is irrational. Find 𝐼(𝑓, 𝛼) and 𝐼(𝑓, 𝛼).
The length of Paulo’s lunch break follows a normal distribution with mean u and standard deviation 5 minutes. On one day in four, on average, his lunch break lasts for more than 52 minutes. (i) Find the value of u. (ii) Find the probability that Paulo’s lunch break lasts for between 40 and 46 minutes on every one of the next four days.
The length of Paulo’s lunch break follows a normal distribution with mean u and standard deviation 5 minutes. On one day in four, on average, his lunch break lasts for more than 52 minutes. (i) Find the value of u.
In a normal distribution, 69% of the distribution is less than 28 and 90% is less than 35. Find the mean
and standard deviation of the distribution
List all the ordered Paris in the relation R=[(a, b) |a divides b ] on the set {1,2,3,4,5,6}.
an investigator predicts that dog owners in the country spend more time walking their dogs than do dog owners in the city. the investigator gets a sample of 21 country owners and 23 city owners. the mean number of hours per week that city owners spend walking their dogs is 10.0. the standard deviation of hours spent walking the dog by city owners is 3.0. the mean number of hours’ country owners spent walking their dogs per week was 15.0. the standard deviation of the number of hours spent walking the dog by owners in the country was 4.0. do dog owners in the country spend more time walking their dogs than do dog owners in the city?
Find number of students securing marks >104, between 155-165, <55 from the following class data.
Class(marks) frequency (students)
0-20 210
20-40 115
40-60 130
60-80 220
80-100 120
100-120 101
120-140 120
140-160 144
160-180 132
180-200 190
Prove that every (relative) extreme value of a function is a stationary value but not every stationary value needs to be an extreme value.
- Check the function f(x,y)=x³-y³+9xy for it's extremum
Given fxx=6x,fxy=0,fyy=6y, find the nature of stationary point at (-1,2)
