STAB22H3 Lecture Notes - Lecture 9: Squared Deviations From The Mean, Probability Distribution, Simple Random Sample

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19 Apr 2018

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Random variable: a random variable is a variable that takes an outcome from a random experiment and gives it a numerical value, ex. Probability distribution: each value of a random variable is an event, so each value has a probability of being obtained, the list of values and probabilities is called probability distribution or probability model. Continuous random variable: random variables considered so far were discrete: we had a list of possible values, such as (cid:1005), (cid:1006), (cid:1007) . The bernoulli model i: a bernoulli random variable has exactly two possible outcomes. We typically label one of these out(cid:272)o(cid:373)es a (cid:862)su(cid:272)(cid:272)ess (cid:271)y (cid:1005) a(cid:374)d a failure (cid:271)y (cid:1004: ex. There is a 70% chance that a student admitted in a graduate program attends the program. We introduce the random variable x such that. The binomial table i: the link to statistical tables includes a table of binomial distribution probabilities.

Related Questions

1. What is a discrete probability distribution? What are the two conditions that determine a probability distribution? What is a discrete probability distribution? Choose the correct answer below

A. A discrete probability distribution exclusively lists probabilities O

B. A discrete probability distribution lists each possible value a random variable can assume. C. A discrete probability distribution lists each possible value a random variable can assume. together with its probability.

D. None of the above

2. What are the two conditions that determine a probability distribution? Choose the correct answer below

A. The probability of each value of the discrete random variable is between 0 and 1, inclusive,

B. The probability of each value of the discrete random variable is between 0 and 1, inclusive.

C. The probability of each value of the discrete random variable is greater than 0 and less than

D. The probability of each value of the discrete random variable is greater than 0 and less than and the sum of all the probabilities is 1. and the sum of all the probabilities can be any amount. 1, and the sum of all the probabilities is 1. 1, and the sum of all the probabilities can be any amount.

azurecamel123

The probability distribution of the random variable X represents the number of hits a baseball player obtained in a game for the 2012 baseball season

x	P(x)
0	0.167
1	0.3289
2	0.2801
3	0.149
4	0.0382
5	0.0368

The probability distribution was used along with statistical software to simulate 25 repetitions of the experiment (25 games). The number of hits was recorded. Approximate the mean and standard deviation of the random variable X based on the simulation. The simulation was repeated by performing 50 repetitions of the experiment. Approximate the mean and standard deviation of the random variable. Compare your results to the theoretical mean and standard deviation. What property is being illustrated?

a.Compute the theoretical mean of the random variable X for the given probability distribution.

Meu = ?

b. Compute the theoretical standard deviation of the random variable X for the given probability distribution.

Sigma =?

c.Approximate the mean of the random variable X based on the simulation for 25 games.

Xbar=?

d. Approximate the standard deviation of the random variable X based on the simulation for 25 games.

S=?

The probability distribution of the random variable X represents the number of hits a baseball player obtained in a game for the 2012 baseball season x P(x) 0 0.167 1 0.3289 2 0.2801 3 0.149 4 0.0382 5 0.0368 The probability distribution was used along with statistical software to simulate 25 repetitions of the experiment (25 games). The number of hits was recorded. Approximate the mean and standard deviation of the random variable X based on the simulation. The simulation was repeated by performing 50 repetitions of the experiment. Approximate the mean and standard deviation of the random variable. Compare your results to the theoretical mean and standard deviation. What property is being illustrated? a.Compute the theoretical mean of the random variable X for the given probability distribution. Meu = ? b. Compute the theoretical standard deviation of the random variable X for the given probability distribution. Sigma =? c.Approximate the mean of the random variable X based on the simulation for 25 games. Xbar=? d. Approximate the standard deviation of the random variable X based on the simulation for 25 games. S=?

oliverabbit290

You are given a fair die, i.e. the outcomes of any throw are contained in the sample space Let the event A be that an even number is thrown and the event B that a multiple of three is thrown. Now consider the two random variables X and Y. X takes on a value of 1 if the event A has occurred and the value 0 if A has not occurred. The random variable Y takes on the value of 1 if the event B has occurred and the value zero if B has not occurred.

(a) Derive the joint pdf of X and Y. Provide this in the form of a table

Y=0 Y=1

X=0
X=1

b) What is the marginal probability distribution of Y?
(c) What is the conditional probability distribution of X, given that Y = 1?
(d) What is E (X|Y = 1)?
(e) What is Cov (X, Y )?
(f) Are X and Y independent random variables?

brownhyena716

STAB22H3 Lecture Notes - Lecture 9: Squared Deviations From The Mean, Probability Distribution, Simple Random Sample

STAB22H3 Full Course Notes

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