In Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a random sample of 1,014 adults aged 18 and over. One of the questions was, "How many cups of coffee, if any, do you drink on an average day?" The following table shows the results obtained: Number of Cups per Day Number of Responses
0 365
1 264
2 193
3 91
4 or more 101
Define a random variable x = number of cups of coffee consumed on an average day. Let x = 4 represent four or more cups.
a. Develop a probability distribution for x.
b. Compute the expected value of x.
c. Compute the variance of x.
d. Suppose we are only interested in adults who drink at least one cup of coffee on an average day. For this group, let y the number of cups of coffee consumed on an average day. Compute the expected value of y and compare it to the expected value of x.

Using the expected value and variance relation, the solutions to the problems posed are given thus :

1.)

Creating a probability distribution function :

X : ____ 0 _____ 1 _____ 2 _____ 3 _____ 4

P(X) _ __ __ __ __

2.)

The Expected value E(X) can be defined thus :

E(X) =

2.)

The Expected Variance Formula :

Var(X) =

Var(X) =

D.)

Expected value of y :

E(X) =

Hence, the expected value of y is greater than of x.

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(b)E(x)=1.3087

(c)Variance of x =1.7119

(d)E(y)=2.0447

Step-by-step explanation:

Random variable x = number of cups of coffee consumed on an average day.

Total Respondents = 1014

(a)Probability distribution for x.

(b)Expected Value of x

E(x)=1.3087

(c)Variance of x

Variance

(d)

E(y)=2.0447

The expected vale of y is greater than the expected value of x.

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step-by-step explanation:

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it