A random variable is defined as a process or variable with a numerical outcome. Which of the following are random variables? i. The amount of rain, in inches, that will fall next Friday in Dallas, TX.
ii. The major of a randomly drawn student from Arizona State University.
iii. The number of books purchased next year by your local library.

a. i only
b. ii only
c. iii only
d. i and iii
e. ii and iii
f. i, ii, and iii

d. i and iii

Step-by-step explanation:

Notice that the definition provided states that the outcome needs to be numerical in order for a variable to be deemed a random variable:

i. The amount of rain is described in inches (i.e. 1.5 in; 2.0 in) and thus may be considered a random variable

ii. The major of a student is not quantitative as it is a descriptive variable (i.e. Arts; Psychology) and thus is not a random variable

iii. The number of books purchased is a numeric quantity (i.e. 15 books) and may be considered a random variable

Therefore, the answer is d. i and iii

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for