These are shorts, so please do 3.1, 3.3 and 3.5b Classify the following random v

Question

These are shorts, so please do 3.1, 3.3 and 3.5b

Classify the following random variables as discrete or continuous: X: the number of automobile accidents per year in Virginia. Y: the length of time to play 18 holes of golf. M: the amount of milk produced yearly by a particular cow. N: the number of eggs laid each month by a hen. P: the number of building permits issued each month in a certain city. Q: the weight of grain produced per acre. An overseas shipment of 5 foreign automobiles contains 2 that have slight paint blemishes. If an agency receives 3 of these automobiles at random, list the elements of the sample space S, using the letters B and N for blemished and nonblemished, respectively: then to each sample point assign a value x of the random variable X representing the number of automobiles with paint blemishes purchased by the agency. Let W be a random variable giving the number of heads minus the number of tails in three tosses of a coin. List the elements of the sample space S for the three tosses of the coin and to each sample point assign a value w of W. A coin is flipped until 3 heads in succession occur. List only those elements of the sample space that require 6 or less tosses. Is this a discrete sample space? Explain. Determine the value c so that each of the following functions can serve as a probability distribution of the discrete random variable X: (a) f(x) = c (x^2 + 4), for x = 0, 1, 2, 3: (b) f(x) = c (2 z) (3 3 - z), for x = 0, 1, 2.

Explanation / Answer

Question 3.1:

a) X: number of automobiles accident per year is a discrete variable as it has a countable number of possible values from 0,1,2,3,4.... and so on

b) Y: Length of time to play 18 holes of golf this is a continuous variable because time is always a continuous variable as time could even have form of fraction and it could even be counted between 2 discrete values for example 2 minutes, 3 minutes therefore could be time values infinite of them in between 2 and 3 minutes as well.

c) M: amount of milk is also a continuout variable as it is clearly uncountable and can have infinite many values.

d) N: Number of eggs laid each month is countable and therefore would be a discrete variable

e) P: Number of building permits issued each month is also countable and therefore would be a discrete variable.

f) Q: Weight is always a continuous variable as it could take infinite many values even between 2 integer weight values.

Question 3.3:

The sample space each element along with the value of W is given as

Sample space element W HHH 3 HHT 2-1 = 1 HTH 2- 1= 1 THH 2- 1= 1 TTH 1 - 2 = -1 THT 1 - 2 = -1 HTT 1 - 2 = -1 TTT 0 - 3 = -3

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