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?

The expectation the instructor to send each day

E(X) = 3.65

Step-by-step 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 with respective probabilities , then the Expectation or Expected value of X  , denoted by E(X) = ∑pi xi

on simplification, we get

E(X) = 3.65

answer: an 8-foot rope is tied from the top of a pole to a

stake in the ground, as shown in the diagram

below

step-by-step explanation: