Question

An online instructor sends updates to students via text. The probability model describes the number of text messages the instructor may send in a day.

Texts Sent 0 1 2 3 4 5

P(X) 0.05 0.05 0.1 0.1 0.4 0.3


How many texts would you expect the instructor to send each day?

Answer 1

The expectation the instructor to send each day

E(X) = 3.65

Explanation:

Given data x : 0 1 2 3 4 5

P(X=x) : 0.05 0.05 0.1 0.1 0.4 0.3

The given data satisfy the two conditions

I) Given all probabilities are p₁(x) ≥0

ii) sum of all probabilities is equal to one

0.05 + 0.05 + 0.1 + 0.1 + 0.4 +0.3 =1

Therefore given data is discrete probability distribution

Expectation :-

suppose a random variable X assumes the values
`x_(1), x_(2),..x_(n)` with respective probabilities
`p_(1), p_(2),..p_(n)` , then the Expectation or Expected value of X , denoted by E(X) = ∑pi xi

`E(X) = 0X0.05+1X 0.05 +2X 0.1 +3X 0.1 +4X0.4 +5X 0.3`

on simplification, we get

E(X) = 3.65