ESE 326 Probability and Statistics for Engineering
Lecture 6
Binomial and Negative Binomial Probability Distributions.
Outcomes of the lecture:
 binomial probability distribution and its characteristics;
 calculating related binomial probabilities using
ESE 326 Probability and Statistics for Engineering
Lecture 21
Testing a hypothesis about and 2
Outcomes of the lecture:
 testing for when is known (zscenario);
 testing for when is unknown (tscenario);
 testing for 2 or (2 test);
Here we apply the
ESE 326 Probability and Statistics for Engineering
Lecture 22
Condence intervals and hypothesis testing for proportions
Outcomes of the lecture:
 sample proportion p and its properties;
 condence interval formula for p;
 formula for the sample size n w
ESE 326 Probability and Statistics for Engineering
Lecture 20
Hypothesis testing: a rejection region approach
Outcomes of the lecture:
 formulating a hypothesis: null and alternative (research) hypotheses;
 Type I and Type II errors and corresponding an
ESE 326 Probability and Statistics for Engineering
Lecture 24
Statistical inference about regression parameters 0 and 1 .
Outcomes of the lecture:
 CI formulas for 1 ;
 performing a test about 1 ;
 CI formulas for 0 ;
 performing a test about 0 ;
 CI
ESE 326 Probability and Statistics for Engineering
Lecture 23
Simple linear regression: estimating the parameters of the best tting
line.
Outcomes of the lecture:
 simple linear regression model;
 least squares method estimates for the linear regression
ESE 326 Probability and Statistics for Engineering
Lecture 7
Hypergeometric and Poisson Probability Distributions.
Outcomes of the lecture:
 hypergeometric probability distribution and its characteristics;
 Poisson probability distribution and its chara
ESE 326 Probability and Statistics for Engineering
Lecture 8
Continuous random variables (crvs) and their probability distributions.
General properties.
Outcomes of the lecture:
 probability density function (pdf) of a crv and its characteristic properti
ESE 326 Probability and Statistics for Engineering
Lecture 11
3 rule and the Chebyshevs inequality. Weibull distribution in the reliability theory.
Outcomes of the lecture:
 3rule for normal distribution;
 Chebyshevs inequality;
 reliability and haza
ESE 326 Probability and Statistics for Engineering
Lecture 12
Introduction to random vectors. Joint probability distribuition function
Outcomes of the lecture:
 joint discrete probability density function and its properties;
 joint continuous probabilit
ESE 326 Probability and Statistics for Engineering
Lecture 10
(Gaussian?"pr663:bilitriTﬂisﬁWiona: 2=aii5tr6x1mat1sn..o£; binomial
distribution: 
Outcomes of the lecture:
 normal probability distribution and its pdf;
— properties of a normal dist
ESE 326 Probability and Statistics for Engineering
Lecture 9
The Gamma probability distrubution.
Outcomes of the lecture:
 Gamma function and its properties;
 pdf of a Gamma probability distribution;
 numerical characteristics of a Gamma probability di
ESE 326 Probability and Statistics for Engineering
Lecture 13
Numerical characteristics of a random vector: covariance and correlation
Outcomes of the lecture:
 covariance as a measure of linear association between X and Y ;
 correlation coecient and it
ESE 326 Probability and Statistics for Engineering
Lecture 17
Point estimation of population parameters: general remarks
Outcomes of the lecture:
 an estimator as a function of a sample;
 unbiased and minimum variance estimators;
 method of moments;

ESE 326 Probability and Statistics for Engineering
Lecture 16
Descriptive statistics. Graphical and numerical characteristics of a sample
Outcomes of the lecture:
 descriptive statistics;
 some graphical summaries of a sample;
 some numerical summaries
ESE 326 Probability and Statistics for Engineering
Lecture 18
Determining distribution of point estimators. Central Limit Theorem
(CLT) and other related results
Outcomes of the lecture:
 mgf mX (t) denes the probability distribution of X;
 some more pr
ESE 326 Probability and Statistics for Engineering
Lecture 15
Transformations of random variables.
Outcomes of the lecture:
 A formula for the pdf of a transformed crv;
 Example: determining the distribution of Z 2 ;
 Distribution of a sum of independe
ESE 326 Probability and Statistics for Engineering
Lecture 19
Condence intervals for parameters and
Outcomes of the lecture:
 condence intervals for when is known;
 sample size formula for estimating when is known;
 condence intervals for when is unkn
ESE 326 Probability and Statistics for Engineering
Lecture 14
Conditional densities and curves of regression
Outcomes of the lecture:
 conditional probability density functions;
 curves of regression;
What we know: If there are two events A and B with k