Hall of Fame - EDB2053: PRP Sept 2016 by Suhaila Hisham

Oct 31

prp_eeutp — 2016-11-07 06:45:05 UTC

SBH: Give 3 important points that you have learnt about identifying discrete random variables. Give your reasons for each.

23208

prp_eeutp — 2016-11-07 06:45:45 UTC

•1. Discrete random variable uses the idea of Bernoulli Trials in which an experiment has two possible outcomes either a 'success' or 'failure'.
2. In an experiment, the trials are independent as they do not affect the outcomes with each other.
3. Lastly, the probabilities of both success and failure are constant throughout the experiment.

22285

prp_eeutp — 2016-11-07 06:45:51 UTC

1-Binomial Distribution- X is the number of 'success' among n trials
2-Poisson Distribution-the probability of x occurrences in an interval
3-Geometric Distribution-X is number of trials to first success

21639

prp_eeutp — 2016-11-07 06:45:58 UTC

•1. all trials are independent for each type of discrete random variables except for hypergeometric

2. order doesn't matter (combination) for binomial & hypergeometric

3. for binomial & poisson, x=0,1,2,3,... while for geometric, x=1,2,3,...

21616

prp_eeutp — 2016-11-07 06:46:03 UTC

1) the trials are independent because the values do not affect the value of the other
2) the set of X values is finite or countably infinite as they cannot be uncountable or it would form a continuous function
3) the pmf (F(x)) is a set of probability values assigned to each value of x as they are discrete values, not continuous

Nov 14

prp_eeutp — 2016-11-21 10:25:36 UTC

SBH: Post your mind map on continuous probability distributions.

21639

2016-11-21 10:27:08 UTC

21639

2016-11-21 10:27:20 UTC

22248

2016-11-21 10:27:34 UTC

20015

2016-11-21 10:27:48 UTC

Sept 21

prp_eeutp — 2016-11-21 10:30:36 UTC

SBH: Give an example of an experiment/observation you can conduct in daily life and describe the sample space you can PROBABLY obtain.

21764 Wong Chun Wei

prp_eeutp — 2016-11-21 10:32:10 UTC

•Gender of student being elected as class student representative

•SS =｛male, female}

21818 Ang Jin S

prp_eeutp — 2016-11-21 10:32:41 UTC

•No.of people buys food from food vending machine in one minute interval

•Sample Space = {0,1,2,...}

23164

prp_eeutp — 2016-11-21 10:33:01 UTC

•The number of times v6 internet fail to connect

•S={0, 1, 2,3,4,5,6,….}

Sept 22

prp_eeutp — 2016-11-21 10:34:04 UTC

SBH: Describe mutually exclusive or disjoint events, in your own words.

23206 Jonathan

prp_eeutp — 2016-11-21 10:35:18 UTC

•Mutually exclusive is where multiple events that does not intersect each other in a given sample space

21951

prp_eeutp — 2016-11-21 10:35:43 UTC

•When two or more events do not intersect each other in a given sample space (each of the event contain unique/different elements)

Sept 28

prp_eeutp — 2016-11-21 10:36:22 UTC

SBH: "In order" or "without order": Which condition will produce a larger sample space? Why?

23208

prp_eeutp — 2016-11-21 10:37:04 UTC

•Having "in order" will produce larger samples size due to the fact that an arrangement of a combination creates a unique outcome in the sample space. Say we have letters X, Y and Z in the sample space, an outcome with arrangement of XYZ is a different outcome than XZY, YXZ, YZX, ZXY or ZYX. e.com/GIAG2.crlox:mozart-app-template

21607

prp_eeutp — 2016-11-21 10:37:27 UTC

•In Order because every order will count as one outcome..

Oct 27

prp_eeutp — 2016-11-21 10:38:40 UTC

SBH: In your own words, explain what variance tells us about a set of data points? How about variance of a probability distribution?

21818

prp_eeutp — 2016-11-21 10:43:03 UTC

•In a set of data point, a variance is the average of the squared differences from Mean. In a probability distribution, a variance measures the spread, variability and distribution.

20015

prp_eeutp — 2016-11-21 10:43:20 UTC

•Variance is a measurement of the spreads between numbers in a data set. The variance measures how far each number in the set is from the mean. Variance is calculated by taking the differences between each number in the set and the mean, squaring the differences (to make them positive) and dividing the sum of the squares by the number of values in the set.

Nov 2

prp_eeutp — 2016-11-21 10:44:56 UTC

SBH: What is continuous random variable?

21720

prp_eeutp — 2016-11-21 10:45:31 UTC

1. the value is obtained by measuring, such as the height of EE student
2. probability distribution showed by density curve
3. The probability that a continuous random variable X is exactly equal to a number is zero
4. takes all value between given intervals of numbers

23208

prp_eeutp — 2016-11-21 10:46:12 UTC

•A continuous random variable is a random variable that has an infinite number of possible values which is the opposite of discrete random variable that can only take certain values. For CRV, it is not necessarily to have every possible number (like from -ve infinity to +ve infinity) but it can be continuous between two values such as 1 and 2 for example. This means CRV could be 1,2 and everything in between 1.00, 1.01, 1.001, 1.001, .....

Nov 7

prp_eeutp — 2016-11-21 10:46:57 UTC

SBH: Compare exponential rv with Poisson rv. Why exponential rv is a continuous rv?

Oct 5

prp_eeutp — 2016-11-21 10:51:52 UTC

SBH: Are mutually exclusive / disjoint events, independent events? Give your reason(s).

21764 Wong Chun Wei

prp_eeutp — 2016-11-21 10:53:00 UTC

Mutually exclusive/disjoint events are not independent events, because:

it does not fulfill the requirement of P(A|B)=P(AnB)/P(B)=P(A).

For the events to be independent, P(AnB)=P(A)P(B) and not equals to 0 as P(A) and P(B) have (non-zero) values.

In this case, there is no intersection and thus P(AnB)=0, resulting in P(A|B)=0, which is not equal to P(A).

Oct 17

prp_eeutp — 2016-11-21 10:54:08 UTC

SBH: Draw a Venn diagram to illustrate a real-life example of 4 mutually exclusive and exhaustive events. Label each event.

21616

prp_eeutp — 2016-11-21 10:56:12 UTC

Miss S: One of the winners. Nice diagram, btw.

Probability of Picking A good or bad fruit out of a basket full of pears and apples placed in a refrigerator in Village 5 D.

There are 4 mutually exclusive events which are:
1) good apple
2) bad apple
3) good pear
4) bad pear

It is impossible to pick an apple that is both good and bad. Likewise, it is impossible to pick a good fruit that is both a pear and an

23185

prp_eeutp — 2016-11-21 10:56:26 UTC

Miss S: One of the winners

The event of getting Spade, Heart, Club and Diamond when choosing a card is mutually exclusive and exhaustive. This is because the event s arena impossible to happened at the same time.

21623

prp_eeutp — 2016-11-21 10:56:38 UTC

Miss S: One of the winners. Thank you for sharing this info with the rest of the class.

Tonight moon phase either it will be
1. Full moon
2. New moon
3. Crecent
4. Gibbous

The moon will never be in two phase at one time unless the world is ending

23197

prp_eeutp — 2016-11-21 10:56:50 UTC

Miss S: A winning observation. Good!

Deleted the old picture. The old venn diagram is wrong because it is not mutually exhaustive events as the sample space aren't specified.

21867

prp_eeutp — 2016-11-21 10:57:04 UTC

SBH: A good observation on the human blood.

21607

prp_eeutp — 2016-11-21 10:57:21 UTC

Miss S: One of the winners. Good representation of the students' dilemma.

A venn diagram about student's preparation before exam and thier results. The venn diagram shows 4 mutually exclusive and exhaustive events..

21764

prp_eeutp — 2016-11-21 11:09:34 UTC

Exponential rv is measured in time domain, where the number of event between a time interval is fixed to 1, the time intervals vary. Poisson rv is measured in number domain, where the time intervals between events are constant, the number of events vary and discrete. Exponential rv is a continuous rv, because the time domain is continuous, the time intervals between events are uncountable. The possible outcome is infinite. Poisson rv: number of patients queing at 5 min interval. Exponential rv: time interval between 2 patients called to see doctor, one patient at a time
.

21553

prp_eeutp — 2016-11-21 11:09:44 UTC

Exponential random variable describes the time between or within Poissons random variable which is continuous yet independent at a constant average rate. An example: The average number of customers in an hours is Poisson BUT the amount of time between a customer and the next one is exponential RV. Since exponential RV can take infinite amount of values of time it is considered continuous.

Nov 9

prp_eeutp — 2016-11-21 11:12:05 UTC

SBH: How does linear transformation Z = (X-µ)/σ affect the normal curve and why do we use it?

23185

prp_eeutp — 2016-11-21 11:13:35 UTC

µ is Mean and σ is Standard Deviation.

Linear transformation is transform a distribution with a given mean and standard deviation into another distribution with mean of 0 and standard deviation of 1.0. The normal curve will be transformed into a STANDARD normal curve.
We can use linear transformation to find the area under the curve or probabilities easily by referring to Standard Normal Distribution Table.

Other than that, we also able to compare the values from different distribution. This can be done by expressing the values as Z and refer to Standard Normal Distribution Table to get the standard value then compare.

21975

prp_eeutp — 2016-11-21 11:14:01 UTC

Linear transformation affect the normal curve by standardizing any P(X=x) that can be expressed with the equivalent in P(Z=z) & computed by using the standard normal table with the parameters of mean(u) and standard deviation(σ) for Z is equal to (X-u)/σ to obtain closed form expression.

Nov 27

prp_eeutp — 2016-11-30 01:30:44 UTC

SBH: Describe the 95% confidence interval (CI) of a mean and give an example how CI can be applied in real life.

23185

prp_eeutp — 2016-11-30 01:32:11 UTC

The 95% confidence interval(CI) of a mean is the population mean has 95% confidence falls in the CI and 5% chances will not falls in the CI. The 5% is distributed into two part which is upper tailed and lower tailed of the standard distribution curve. The CI is estimated with sample size and sample mean.

Besides, no estimate can have 100% reliability to represent the whole population hence 95% CI means the CI has 95% reliability that the population mean will falls in the interval. CI can applied in real life for example, a business might estimate that a machine uses 10 lbs. of plastic for each unit of a product created. Because the machine cannot be expected to use precisely 10 lbs. per unit, a confidence interval can be created to give a range of possibilities. The company might predict that there is a 95 percent chance that the machine uses on average between 9.85 and 10.5 lbs. of plastic per unit. The confidence interval in this example is 95 percent, and the likelihood that the actual amount of plastic used is outside the estimated range is 5 percent.

23136

prp_eeutp — 2016-11-30 01:37:30 UTC

A cl gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.
Example: student measuring the boiling temperature of a certain liquid observes the readings (in degrees Celsius) 102.5, 101.7, 103.1, 100.9, 100.5, and 102.2 on 6 different samples of the liquid. He calculates the sample mean to be 101.82. If he knows that the standard deviation for this procedure is 1.2 degrees, what is the confidence interval for the population mean at a 95% confidence level?

22193

prp_eeutp — 2016-11-30 01:38:53 UTC

The confidence interval describes the uncertainty associated with a sampling method. Suppose we used the same sampling method to select different samples and to compute a different interval estimate for each sample. Some interval estimates would include the true population parameter and some would not. A 90% confidence level means that we would expect 90% of the interval estimates to include the population parameter; A 95% confidence level means that 95% of the intervals would include the parameter.For example, “For the European data, one can say with 95% confidence that the true population for wellbeing among those without TVs is between 4.88 and 5.26.” The confidence interval here is “between 4.88 and 5.26“.

22248

prp_eeutp — 2016-11-30 01:41:13 UTC

Interval (CL, CU) is the confidence interval (CI) such that an intended parameter (mean/ variance/ standard deviation). 95% CI of a mean is having a significance level alpha=5%. Alpha is the critical region or aka the possible error for the mean to be in the interval while (1-alpha)*100 is the confidence level which we confident the mean lies in the particular interval. CI can be applied in real life such as the interval of the weight of 100 students out of all UTP students.

21698

2016-12-14 02:42:30 UTC

21616

jpp3596 — 2016-12-14 02:42:45 UTC

A child is playing with a Transformers figure which can transform into 3 modes, "car”, “helicopter” and “robot”. The observation is such that the mode of the Transformers figure is noted at every minute.

Labelling the state space {1 = robot, 2 = car, 3 = helicopter} the transition matrix for this example is

P = | 0.9 0.075 0.025 |

| 0.15 0.8 0.05 |
| 0.25 0.25 0.5 |

Inspiration taken from: https://en.wikipedia.org/wiki/Markov_chain#/media/File:Finance_Markov_chain_example_state_space.svg

Dec 7

prp_eeutp — 2016-12-14 02:43:24 UTC

SBH: Draw a Markov chain diagram for a real-life example. (Probabilities need not be exact)

22181

prp_eeutp — 2016-12-14 02:53:36 UTC

Significance level is the probability of when the null hypothesis is true.
Alpha set the range of data before we can reject the null hypothesis.
P-value show what is the value the data falls at.

Nov 30

prp_eeutp — 2016-12-14 02:54:23 UTC

SBH: What is the difference between level of significance, α and p-value?

22129

prp_eeutp — 2016-12-14 02:56:32 UTC

Alpha sets the standard for how extreme the data must be before we can reject the null hypothesis. The p-value indicates how extreme the data are. We compare the p-value with the alpha to determine whether the observed data are statistically significantly different from the null hypothesis:
-If the p-value is less than or equal to the alpha (p< .05), then we reject the null hypothesis, and we say the result is statistically significant.
- If the p-value is greater than alpha (p > .05), then we fail to reject the null hypothesis, and we say that the result is statistically nonsignificant.