Warm-up 2. Suppose that in an experiment we randomly select 5 students from ourclass, one after the other. Let us call our random sample of students ω = (S1, S2, S3, S4, S5),where Si is the i-th selected student.(a) Come up with a random variable X (you may be creative here!) that assigns anumber to each random sample of students ω.(b) What would be the range of your random variable X?(c) Let k be an arbitrary number from the range of X. Explain the meaning ofP(X = k) for the random variable you defined (you do not need to calculate thisquantity)

A population consists of the following N = 5 numbers: 2, 5, 6, 9, 27. Suppose a randomsample of size n = 3 is selected without replacement from this population.(a) [5 marks] Determine the sampling distribution of the sample range. Note that therange of a set of values is defined to be the difference between the largest value andthe smallest value

The set whose elements are the numbers assigned to the outcomes of a random event or an experiment.*ProbabilityRandom VariableMass functionExpected valueNone of the above

a range of values so defined that there is a specified probability that the value of a parameter lies within it.

(a)A manager at a bus company wants to survey employees about the new uniforms. Which of the following best describes a random sample of employees?The manager asks for volunteers and selects every volunteer until 60 employees are selected. She selects the volunteers because these employees are easily accessible.The manager forms groups of 12 employees based on the departments the employees are in. Then, she selects all of the employees in 5 randomly chosen groups.The manager uses a computer program to draw 60 employees at random and selects these employees. Every set of 60 employees is equally likely to be drawn by the computer program.(b)A consultant wants to ask workers at a factory about the workers' job satisfaction. Which of the following best describes a stratified sample of workers?The consultant forms groups of 8 workers based on the lengths of time the workers have worked at the factory. Then, he randomly chooses 9 groups and selects all of the workers in these groups.The consultant assigns each worker a different number. Using a random number table, he draws 72 of those numbers at random. Then, the consultant selects the workers assigned to the drawn numbers. Every set of 72 workers is equally likely to be drawn using the random number table.The consultant forms 6 groups of workers based on the workers' shifts. Then, he selects 12 workers at random from each group.(c)A city manager wants to poll residents about a park renovation. Which of the following best describes a convenience sample of residents?The city manager takes a list of the residents and selects every 5th resident until 90 residents are selected.The first 90 residents who walk into city hall one day are easily accessible. So, the city manager selects these residents.The city manager forms 5 groups of residents based on the residents' incomes. Then, she selects 18 residents at random from each group.

Which of the following is correct to obtain a random integer between 5 and 10 (inclusive)?